I do not get the correct Binding syntax to access the Cats and Dogs properties of MyViewModel within a DateTemplate that
Try giving your ListBox a name and refer to its DataContext in the bindings:
<ListBox x:Name="myList" ItemsSource="{DynamicResource MyColl}">
<ListBox.Resources>
<CompositeCollection x:Key="MyColl">
<CollectionContainer Collection="{Binding DataContext.Dogs, Source={x:Reference myList}}"/>
<CollectionContainer Collection="{Binding DataContext.Cats, Source={x:Reference myList}}"/>
</CompositeCollection>
</ListBox.Resources>
</ListBox>
Due to the issue with data binding on CollectionContainer as described http://social.msdn.microsoft.com/Forums/vstudio/en-US/b15cbd9d-95aa-47c6-8068-7ae9f7dca88a/collectioncontainer-does-not-support-relativesource?forum=wpf I now use the following approach:
<ListBox>
<ListBox.Resources>
<CollectionViewSource x:Key="DogCollection" Source="{Binding Dogs}"/>
<CollectionViewSource x:Key="CatCollection" Source="{Binding Cats}"/>
</ListBox.Resources>
<ListBox.ItemsSource>
<CompositeCollection>
<CollectionContainer Collection="{Binding Source={StaticResource DogCollection}}"/>
<CollectionContainer Collection="{Binding Source={StaticResource CatCollection}}"/>
</CompositeCollection>
</ListBox.ItemsSource>
<!-- ... -->
</ListBox>
Edit: The CompositeCollection class does not derive from FrameworkElement and thus does not have a DataContext property to support data binding. It will only work if you use Binding providing a Source. Have a look here https://stackoverflow.com/a/6446923/1254795 for more information.