Stopping WPF TextBox from growing with text

I am trying to modify my simple control so that the text box does not grow as the user types in long text. I took a look at some solutions posted here at Stackoverflow that suggest using a Grid and an invisible Border and binding the Width of the text box to the ActualWidth of the Border, but I can't seem to get it to work in my setup.

Here is the xaml of my control:

<StackPanel Margin="5,0">
<WrapPanel Margin="0,0,0,5">
  <TextBlock Foreground="White" Margin="0,0,2,0">TEXT</TextBlock>
  <TextBlock Foreground="#FF0099CC" FontWeight="Bold">MORE TEXT</TextBlock>
</WrapPanel>
<Border Margin="2,4,0,4" BorderThickness="1" SnapsToDevicePixels="True" Background="Black"
        BorderBrush="{DynamicResource {x:Static SystemColors.ControlDarkBrushKey}}">
  <StackPanel Orientation="Horizontal">
    <Image Source="..\Resources\zoom.png" Width="13"/>
    <TextBox Foreground="White" Background="Black" BorderBrush="Transparent">THIS IS SOME TEXT</TextBox>
  </StackPanel>
</Border>
</StackPanel>

Any ideas? I need the zoom.png to appear "inside" of the text box so I use a horizontal stack panel and just place the image and text box side by side, both surrounded by the same border.

Is there a way for me to stop my text box from auto growing as text is typed?

Thanks.

UPDATE:

Below is the xaml I am testing with.

<Window x:Class="Desktop.Shell"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:composite="http://www.codeplex.com/CompositeWPF"
    Title="MyShell" Height="50" Width="900"
    WindowStyle="None"
    ShowInTaskbar="False"        
    AllowsTransparency="True"
    Background="Transparent"
    ResizeMode="CanResizeWithGrip"
    WindowStartupLocation="CenterScreen">
  <Border BorderB