I don't want to leave you waiting too long. The short answer is that the issue is with the Clip Children checkbox. Clip Children is a wrapper for GUI.BeginGroup() ... GUI.EndGroup(), which sets up clipping and temporarily adjusts the GUI coordinate system to the parent's rect bounds.
When Clip Children is off, the Dialogue System manually offsets the children instead. Something funny is happening here with nested children. I'm looking into what's going on. If it turns out to be an issue with the Dialogue System's manual offset code, I'll issue a patch. Otherwise I'll explain how to fix your UI.
I also just emailed you a working example scene where Clip Children is ticked.
Portrait Image Moving after first line of text.
Portrait Image Moving after first line of text.
This was a bug that affects versions up to 1.4.6.1. The fix is in the upcoming version 1.4.7.