We have some API that wires up editor views to support IME. It should enable/disable it based on if the view has keyboard focus (EditorView.GotKeyboardFocus event, etc.). I would think that it would disable its own IME implementation if your TextBox has keyboard focus since in that case the view wouldn't have focus. And I would hope that it wouldn't interfere with your TextBox's IME in that case either.
We do call InputMethod.SetIsInputMethodSuspended(view, true) when the view is created meaning it suspends normal IME at that level. We need to do that to get our own custom IME working since Microsoft doesn't make it easily available for anything other than TextBox and RichTextBox. Perhaps that setting is blocking your TextBox's IME from being supported since it's a child visual. In that case, I'm not sure if there will be a workaround. You might try setting that attached property to false on the view when your TextBox is going to get focus to see if that helps. Then back to true when it loses focus.
If you'd like us to look into it further, yes, please submit a new simple sample project that shows the issue. Rename the .zip file extension so it doesn't get spam blocked. Thanks!