I'd bring it to another shop - there's no reason they shouldn't be able to give an estimate. (many insurance companies will take the estimates from body shops that are on their approved list, too...) It's all done based on book rates - they look at what needs replaced, and the system tells them how much it costs to do it.
Once they get started, the body shop will work with the insurance company if there are any other parts damaged, etc. - as long as it's a decent shop with a good reputation, you should be just fine. If it's a shady shop, well... go somewhere else!