A: 

Thanks to this post I was able to get this to work. I set the StackPanel around the text box to bind to the selected item, then bound the text box to the property I care about.

<StackPanel DataContext={Binding ElementName=myTreeView, Path=SelectedItem}">
    <TextBox Text={Binding Path=SomeOtherProperty, Mode=TwoWay}" />
</StackPanel>

Works like a charm.

Adam