I am sorry you are having problems with your new insurance. Most insurances have nurses that work for them to answer medical questions and such. I would start there, find out if there are nurses that can talk to you about the insurance aspect of a VBAC.
The first thing you need to do is set up a time to tour your choosen hospital. It really doesn't matter what your doctor thinks or the policies of the hospital you plan on going to will not allow it. You need to ask a few things, if they allow VBACs, their rate and any special rules that apply to women attempting VBAC (such as not allowing a woman to attempt if they have had X many c-sections).
Next I would make an appointment with your doctor, let schedular know that you have a lot of questions and would most likely require a longer appointment then a regular check. Ask specifically about office policies and how they feel about VBACs. Come with questions written down and leave enough space to jot down notes. You can also ask them if there is anything they can suggest to read to get your prepared for a VBAC.
It's important to balance having a voice with reverence for their knowledge.
Good luck and I hope everything goes well.