Wpf – How to make the StackPanel or DockPanel stretch to fit their containers in WPF

I have a Grid as a root container with two columns defined (There's only one row).
The first column has flexible width and second column has 300px fixed width.
Next, I have placed a ListBox inside the second column to stretch both horizontally and vertically, i.e. to fill the entire second column.
Lastly, I have defined an Items Template for the ListBox to be a vertically oriented StackPanel, with one DockPanel and a couple of TextBlocks inside.

<!-- Data template for ListBox -->
<DataTemplate DataType="{x:Type entities:Track}">
  <StackPanel Orientation="Vertical">
    <DockPanel>
      <TextBlock DockPanel.Dock="Left" Text="Now playing" />
      <TextBlock DockPanel.Dock="Right" Text="Time remaining" />
    </DockPanel>
    <TextBlock Text="{Binding Artist}" />
    <TextBlock Text="{Binding Title}" />
  </StackPanel>
</DataTemplate>

...

<ListBox 
  Grid.Column="1" 
  HorizontalAlignment="Stretch" 
  VerticalAlignment="Stretch" />

I have two questions:

1. How do I make the StackPanel fill the entire width of the ListBox? Right now, it only takes enough space to accomodate the DockPanel and the TextBlocks inside. It won't fit the width of the ListBox or ListBoxItem.
2. Next, how do I make the DockPanel fill the entire width of the StackPanel, i.e. its parent? What happens right now is that even if the width of the TextBlocks in the StackPanel exceed the width of the DockPanel, it won't stretch to match their width.

Thanks for the help.