Wow. I can see why you're stressing out. It's curious that Dr. M. is "seriously booked up" and Dr. R. has plenty of appointment times. :D It's wonderful that Dr. M. helped write the hospital policy allowing vbac. Should you go into labor and Dr. R. is oncal and won't let you vbacl, BY LAW the hospital has to find you another dr if you request one!
For what it's worth, I had a VBAC 10 years ago with the extremely unsupportive doctor on call. I learned a couple years later that the two OBs were no longer working together, but that the practice at that time (shortly before I had to move out of town) consisted of one OB/Gyn and several midwives.
What did I do? Well, I took the best childbirth class I could find , but not particularly because of the doctor; The doctor I liked delivered the first child, and it was "pre-labor" issues that she couldn't have done anything about. So I had the misfortune to go into labor on Saurday night when it was the other doctor's turn to cover.