Go back to the insurance company. Get the name of the person you speak with and log it - date and time of call - as well as the nature of the call. Ask her to follow up the conversation with a letter confirming their ability to pay, the guarantee the dentist office signs and what the insurance will do in this case.
Your questions should be:
the dentist refuses to guarantee their surgery. I have been told the dentist office signs a form guaranteeing their work. Can they provide that guarantee?
The dentist office stated that you will not allow them to bill twice for the same procedure. There are different dates on this procedure, what is your stance, will you pay twice?
We would like to go to another dentist within network due to these issues, can you recommend one and also can you confirm that the procedure will be paid?
Get everything in writing. Get another dentist within your network and ensure, in writing, that they will pay for the procedure again due to the problems at hand.
Good luck!