Unfortunately, I suspect this is a low-end, or substandard carrier. They often try to bully you into accepting low end fixes or after market parts.
The law does not require this.
What you should do, assuming this is your own company, is get two estimates, then take it to your preferred body shop. Unfortunately, you may not get dollar for dollar what you are being charged. Reporting them to the Illinois Department of Insurance is pretty useless, although you can try. Talking to a supervisor at the insurer may help too.
YOU DO NOT HAVE TO USE THEIR MECHANIC.
But they don't necessarily have to pay the charges at your mechanic. They only have to pay reasonable cost to repair, which is not written in stone.
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You should be able to bring your vehicle into the body shop of your own choosing, unless stated otherwise in your policy of insurance. Once the vehicle is at the body shop, the insurance company can deal directly with the shop.
You don't say whether this is your own insurer, but assuming it is be sure to read your policy to see what your rights are. If the insurer is not honoring the terms of the policy you may wish to contact the Illinois Department of Insurance, which you can do at this website: https://mc.insurance.illinois.gov/messagecenter.nsf.
Most insurance policies provide compensation for reasonable damages. Their choice of mechanic may establish what reasonable damages are in the mind of the insurance company. I would take it to their mechanic for an estimate and then get two more estimates from mechanics you prefer. If they are all in the same ballpark, then your insurer may relent. READ the terms of the policy to make sure whether under their contract of insurance they can choose the mechanic. Policies are hard to read, and you may want to spend a couple hundred dollars on an attorney if a fair amount of money is at stake.
carefully read the policy language. It is unlikely that you will be required to use the repair shop chosen by the insurance carrier, but they will not be responsible for excessive charges that the shop of your choice may decide to charge. The carrier is responsible for the repair of your vehicle. Oftentimes, it comes down to what a reasonable charge would be for the necessary repair to your vehicle in the community in which you live. You don't have to accept the cheapest repair shop, and they don't have to pay for the most expensive shop in town.