5. Qd2 seems like a mistake to me. What's the point? Before Qd2, O-O would remove the pin. After Qd2, O-O still leaves the knight pinned (now just to the queen).
If you want to move the queen, 5. Qc2 seems more reasonable to me. And after 5. Qc2, black can't play 5... Ne4 because the queen will hang.
My favourite move after Bb4 is Qb3. If Bxc3 then bxc3 threatning Bxf6.
It doesn't look that terrible, after Bxd8 Nxd2 Kxd2 but it's certainly not ideal either. In general, you don't want your queen to block the pin as that often makes the pin even harder to break, unless you have a really good reason. Why not just play Qc2 or Qb3? They're much less risky.
Or Bxc3 before Nxd2
5.Qd2 is a mistake because allows the black knight attack the queen. The queen must go to c2 where prevents the previous move and also not pinned by the bishop. Also controls the c file after Rc1
Try 5. Q-b3
I would go with KnF3. Your trying to stop one pin with another. I suppose if the bishop bothers you A3.
I've been having a lot of trouble with this! How does white play on from here? Or was there a mistake earlier?