Deje que el cuadro de texto se extienda para rellenar el ancho en StackPanel

No estoy seguro a qué elemento pones HorizontalAlignment, pero esto es lo que funciona para mí:

<StackPanel>
    <TextBlock Text="Title" Style="..."/>
    <TextBlock Margin="0,0,0,10" Text="Description" Style="..."/>
    <TextBox HorizontalAlignment="Stretch" />
    <Button Margin="0" Content="Save"/>
</StackPanel>

Esto extiende el TextBox a todo el ancho del StackPanel.

Se encontró con esta pregunta mientras buscaba si existía un DockPanel de WinRT.

Terminé modificando ligeramente el DockPanel que viene con el Kit de herramientas Silverlight, y parece funcionar.

Para usar, agregue xmlns:toolkit="using:System.Windows.Controls" a la parte superior, y tomando la pregunta anterior como escenario, podríamos escribir:

<toolkit:DockPanel Width="400">
    <TextBlock Text="Label" Width="150" toolkit:DockPanel.Dock="Left" />
    <TextBox Text="Value" />
</toolkit:DockPanel>

DockPanel.cs:

// (c) Copyright Microsoft Corporation.
// This source is subject to the Microsoft Public License (Ms-PL).
// Please see http://go.microsoft.com/fwlink/?LinkID=131993 for details.
// All other rights reserved.

// Modified slightly for Windows Runtime support.

using System;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.IO;
using System.Linq;
using Windows.Foundation;
using Windows.Foundation.Collections;
using Windows.UI.Xaml;
using Windows.UI.Xaml.Controls;
using Windows.UI.Xaml.Controls.Primitives;
using Windows.UI.Xaml.Data;
using Windows.UI.Xaml.Input;
using Windows.UI.Xaml.Media;
using Windows.UI.Xaml.Navigation;

namespace System.Windows.Controls
{
    public enum Dock
    {
        // Summary:
        //     Specifies that the control should be positioned on the left of the control.
        Left = 0,
        //
        // Summary:
        //     Specifies that the control should be positioned on top of the control.
        Top = 1,
        //
        // Summary:
        //     Specifies that the control should be positioned on the right of the control.
        Right = 2,
        //
        // Summary:
        //     Specifies that the control should be positioned at the bottom of the control.
        Bottom = 3,
    }

    /// <summary>
    /// Arranges child elements around the edges of the panel.  Optionally, 
    /// last added child element can occupy the remaining space.
    /// </summary>
    /// <QualityBand>Stable</QualityBand>
    public class DockPanel : Panel
    {
        /// <summary>
        /// A value indicating whether a dependency property change handler
        /// should ignore the next change notification.  This is used to reset
        /// the value of properties without performing any of the actions in
        /// their change handlers.
        /// </summary>
        private static bool _ignorePropertyChange;

        #region public bool LastChildFill
        /// <summary>
        /// Gets or sets a value indicating whether the last child element
        /// added to a <see cref="T:System.Windows.Controls.DockPanel" />
        /// resizes to fill the remaining space.
        /// </summary>
        /// <value>
        /// True if the last element added resizes to fill the remaining space,
        /// false to indicate the last element does not resize. The default is
        /// true.
        /// </value>
        public bool LastChildFill
        {
            get { return (bool)GetValue(LastChildFillProperty); }
            set { SetValue(LastChildFillProperty, value); }
        }

        /// <summary>
        /// Identifies the
        /// <see cref="P:System.Windows.Controls.DockPanel.LastChildFill" />
        /// dependency property.
        /// </summary>
        public static readonly DependencyProperty LastChildFillProperty =
            DependencyProperty.Register(
                "LastChildFill",
                typeof(bool),
                typeof(DockPanel),
                new PropertyMetadata(true, OnLastChildFillPropertyChanged));

        /// <summary>
        /// LastChildFillProperty property changed handler.
        /// </summary>
        /// <param name="d">DockPanel that changed its LastChildFill.</param>
        /// <param name="e">Event arguments.</param>
        private static void OnLastChildFillPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
        {
            DockPanel source = d as DockPanel;
            source.InvalidateArrange();
        }
        #endregion public bool LastChildFill

        #region public attached Dock Dock
        /// <summary>
        /// Gets the value of the
        /// <see cref="P:System.Windows.Controls.DockPanel.Dock" /> attached
        /// property for the specified element.
        /// </summary>
        /// <param name="element">
        /// The element from which the property value is read.
        /// </param>
        /// <returns>
        /// The <see cref="P:System.Windows.Controls.DockPanel.Dock" /> property
        /// value for the element.
        /// </returns>
        [SuppressMessage("Microsoft.Design", "CA1011:ConsiderPassingBaseTypesAsParameters", Justification = "DockPanel only has UIElement children")]
        public static Dock GetDock(UIElement element)
        {
            if (element == null)
            {
                throw new ArgumentNullException("element");
            }
            return (Dock)element.GetValue(DockProperty);
        }

        /// <summary>
        /// Sets the value of the
        /// <see cref="P:System.Windows.Controls.DockPanel.Dock" /> attached
        /// property for the specified element to the specified dock value.
        /// </summary>
        /// <param name="element">
        /// The element to which the attached property is assigned.
        /// </param>
        /// <param name="dock">
        /// The dock value to assign to the specified element.
        /// </param>
        [SuppressMessage("Microsoft.Design", "CA1011:ConsiderPassingBaseTypesAsParameters", Justification = "DockPanel only has UIElement children")]
        public static void SetDock(UIElement element, Dock dock)
        {
            if (element == null)
            {
                throw new ArgumentNullException("element");
            }
            element.SetValue(DockProperty, dock);
        }

        /// <summary>
        /// Identifies the
        /// <see cref="P:System.Windows.Controls.DockPanel.Dock" />
        /// attached property.
        /// </summary>
        public static readonly DependencyProperty DockProperty =
            DependencyProperty.RegisterAttached(
                "Dock",
                typeof(Dock),
                typeof(DockPanel),
                new PropertyMetadata(Dock.Left, OnDockPropertyChanged));

        /// <summary>
        /// DockProperty property changed handler.
        /// </summary>
        /// <param name="d">UIElement that changed its Dock.</param>
        /// <param name="e">Event arguments.</param>
        [SuppressMessage("Microsoft.Usage", "CA2208:InstantiateArgumentExceptionsCorrectly", Justification = "Almost always set from the attached property CLR setter.")]
        private static void OnDockPropertyChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
        {
            // Ignore the change if requested
            if (_ignorePropertyChange)
            {
                _ignorePropertyChange = false;
                return;
            }

            UIElement element = (UIElement)d;
            Dock value = (Dock)e.NewValue;

            // Validate the Dock property
            if ((value != Dock.Left) &&
                (value != Dock.Top) &&
                (value != Dock.Right) &&
                (value != Dock.Bottom))
            {
                // Reset the property to its original state before throwing
                _ignorePropertyChange = true;
                element.SetValue(DockProperty, (Dock)e.OldValue);

                string message = string.Format(
                    CultureInfo.InvariantCulture,
                    "InvalidValue",
                    value);
                throw new ArgumentException(message, "value");
            }

            // Cause the DockPanel to update its layout when a child changes
            DockPanel panel = VisualTreeHelper.GetParent(element) as DockPanel;
            if (panel != null)
            {
                panel.InvalidateMeasure();
            }
        }
        #endregion public attached Dock Dock

        /// <summary>
        /// Initializes a new instance of the
        /// <see cref="T:System.Windows.Controls.DockPanel" /> class.
        /// </summary>
        public DockPanel()
        {
        }

        /// <summary>
        /// Measures the child elements of a
        /// <see cref="T:System.Windows.Controls.DockPanel" /> in preparation
        /// for arranging them during the
        /// <see cref="M:System.Windows.Controls.DockPanel.ArrangeOverride(System.Windows.Size)" />
        /// pass.
        /// </summary>
        /// <param name="constraint">
        /// The area available to the
        /// <see cref="T:System.Windows.Controls.DockPanel" />.
        /// </param>
        /// <returns>
        /// The desired size of the
        /// <see cref="T:System.Windows.Controls.DockPanel" />.
        /// </returns>
        [SuppressMessage("Microsoft.Naming", "CA1725:ParameterNamesShouldMatchBaseDeclaration", MessageId = "0#", Justification = "Compat with WPF.")]
        protected override Size MeasureOverride(Size constraint)
        {
            double usedWidth = 0.0;
            double usedHeight = 0.0;
            double maximumWidth = 0.0;
            double maximumHeight = 0.0;

            // Measure each of the Children
            foreach (UIElement element in Children)
            {
                // Get the child's desired size
                Size remainingSize = new Size(
                    Math.Max(0.0, constraint.Width - usedWidth),
                    Math.Max(0.0, constraint.Height - usedHeight));
                element.Measure(remainingSize);
                Size desiredSize = element.DesiredSize;

                // Decrease the remaining space for the rest of the children
                switch (GetDock(element))
                {
                    case Dock.Left:
                    case Dock.Right:
                        maximumHeight = Math.Max(maximumHeight, usedHeight + desiredSize.Height);
                        usedWidth += desiredSize.Width;
                        break;
                    case Dock.Top:
                    case Dock.Bottom:
                        maximumWidth = Math.Max(maximumWidth, usedWidth + desiredSize.Width);
                        usedHeight += desiredSize.Height;
                        break;
                }
            }

            maximumWidth = Math.Max(maximumWidth, usedWidth);
            maximumHeight = Math.Max(maximumHeight, usedHeight);
            return new Size(maximumWidth, maximumHeight);
        }

        /// <summary>
        /// Arranges the child elements of the
        /// <see cref="T:System.Windows.Controls.DockPanel" /> control.
        /// </summary>
        /// <param name="arrangeSize">
        /// The area in the parent element that the
        /// <see cref="T:System.Windows.Controls.DockPanel" /> should use to
        /// arrange its child elements.
        /// </param>
        /// <returns>
        /// The actual size of the
        /// <see cref="T:System.Windows.Controls.DockPanel" /> after the child
        /// elements are arranged. The actual size should always equal
        /// <paramref name="arrangeSize" />.
        /// </returns>
        [SuppressMessage("Microsoft.Naming", "CA1725:ParameterNamesShouldMatchBaseDeclaration", MessageId = "0#", Justification = "Compat with WPF.")]
        protected override Size ArrangeOverride(Size arrangeSize)
        {
            double left = 0.0;
            double top = 0.0;
            double right = 0.0;
            double bottom = 0.0;

            // Arrange each of the Children
            UIElementCollection children = Children;
            int dockedCount = children.Count - (LastChildFill ? 1 : 0);
            int index = 0;
            foreach (UIElement element in children)
            {
                // Determine the remaining space left to arrange the element
                Rect remainingRect = new Rect(
                    left,
                    top,
                    Math.Max(0.0, arrangeSize.Width - left - right),
                    Math.Max(0.0, arrangeSize.Height - top - bottom));

                // Trim the remaining Rect to the docked size of the element
                // (unless the element should fill the remaining space because
                // of LastChildFill)
                if (index < dockedCount)
                {
                    Size desiredSize = element.DesiredSize;
                    switch (GetDock(element))
                    {
                        case Dock.Left:
                            left += desiredSize.Width;
                            remainingRect.Width = desiredSize.Width;
                            break;
                        case Dock.Top:
                            top += desiredSize.Height;
                            remainingRect.Height = desiredSize.Height;
                            break;
                        case Dock.Right:
                            right += desiredSize.Width;
                            remainingRect.X = Math.Max(0.0, arrangeSize.Width - right);
                            remainingRect.Width = desiredSize.Width;
                            break;
                        case Dock.Bottom:
                            bottom += desiredSize.Height;
                            remainingRect.Y = Math.Max(0.0, arrangeSize.Height - bottom);
                            remainingRect.Height = desiredSize.Height;
                            break;
                    }
                }

                element.Arrange(remainingRect);
                index++;
            }

            return arrangeSize;
        }
    }
}

Caminé a través de este desierto durante 10 minutos u horas, y descubrí que el mejor control nativo para pulir el contenido es la cuadrícula de mi snipet que funciona bien:

<Grid >
   <TextBox x:Name="txtCountry" Margin="0,8,41,8" />
   <Button x:Name="btnGetCountry" Content="..." Margin="0,8,0,8"  HorizontalAlignment="Right"  Click="btnGetCountry_Click"> </Button>
</Grid>

Esto generará un buen diseño adaptable con un cuadro de texto steching y un butoon en su lado que mantiene su aspecto