I did that once myself too, for a couple years long ago. It was quite a headache. How attached are you to her? I think what she's suggesting is quite reasonable, but not easy for you, and I'd consider switching unless you're particularly enamored.

As far as reimbursement, you might ask your insurance agent about the details, worst case scenario, reimbursement can take a few months, but some companies are able to do it, in some situations, as quickly as a couple weeks. However, if it's a financial hardship, I would again suggest trying to find someone in-network unless you can't bear to leave her.