Sadly, this is one of the potential pitfalls of trying to handle a car accident claim on your own. Normally, I would encourage you to consult an attorney directly (more details are needed to answer your question, and an experienced lawyer would be able to help tailor a response on your particular situation), but it's difficult to find a lawyer to handle a case at this stage.
This response is based on limited information. It is not meant as and does not constitute legal advice and does not create an attorney-client relationship.
Get it out of the shop ASAP because you are incurring charges. You can always fix this issue later. Are you injured? If you are most attorneys can help you out with getting this disputed reimbursed.
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The other counsel gave you good advice. Pay them from your pocket, and start driving it instead of incurring more cost. You can always fight with the insurance company and the body shop. If they had accepted the estimate, they should not have any problem paying them. The insurance company's adjusters are expert in these issues, many of them are themselves body shop people.
Only see a licensed attorney before you make any decision. This answer may not be perfect in any given situation. However, more fact may be required by your local attorney.