Could you specify whether you are talking about the emergency room doctor. And can you tell us if you have spoken directly with the doctor, his staff, or his billing service? In the meantime:
The responsibility for making payment for services rendered to your wife most likely lies with you. If you signed paperwork in the emergency room, chances are that you signed an agreement to be responsible for payment for those services rendered.
Providers who participate as Medicare doctors are required to file an insurance claim on behalf of the Medicare patient they see. So far as I know, doctors are not required to file insurance claims on behalf of anyone else. They are free to require payment from the one who is financially responsible for the patient. Doctors are also free to send the responsible party to collections if they don't pay for the services rendered.
If a doctor chooses to not bill your insurance carrier for you, you cannot force him to. All you can do is pay your bill (or make monthly payments) and send a copy of the doctor's fee slip to your insurance carrier for reimbursement.
You might contact the doctor's billing service if you haven't talked with them already. Explain your situation, tell them what insurance you have, ask if they are a participating provider, and ask if they would consider billing the insurance company for you. If they won't submit a bill for you to your insurance carrier, you might ask if you could make monthly payments. If you have spoken with the billing service, but not with the doctor, you might try to talk to the doctor and tell him how his billing service is handling you. He can't know these kinds of things unless he gets feedback from patients.