I do think it's the Lord's decision, not the Duke's.
When the Duke (Duchy A) becomes Lord of a region in another Duchy (B), it will become part of his own Duchy (A) though, I think. At least I've had the case that when being lord in duchy B, then being appointed as duke of duchy A, the region obviously joined duchy A as well.
Is this at all clear? 
Any confirmation on that might be needed though. Allegiances have changed a lot, when I was gone and while I was already back. So I could have missed something.
Your understanding is same as mine. Cannot even ask Duke Duchy B of a region to change that region back to Duchy A. Look like we gonna end up with more and more regions suppose in Duchy B but belong to Duchy A. Unless we ask the region lord to step down before we appoint as duke. Unless we ask the new region lord to change allegiance from Duchy A to Duchy B. Hmmmm, I need play the fealty mechanics here if that is the case.
