While I personally believe the second MW should get the money, that's not how it works in the real world.
We changed doctors over halfway through my pregnancy but only got back about 10% of the payments I paid the first doctor (ante-natal + delivery costs) and still had to pay the second doctor her full fee (ante-natal + delivery + post-partum care). My first doc did NOTHING for us yet we paid her a hefty chunk of change.
My situation is hard to explain, like yours, but I wish you all the best! I hope it works out in your favor!
From my iPhone, probably while BF'ing.