No there is not law that you much take your wrecked vehicle to your insurance company's referred body or repair shop.

In Illinois you are not required to use the insurance company's preferred shop, or any that they referred you to. According to the IL Department of Insurance you are not required to use your company's suggested repair shop for your damaged vehicle to be fixed. So you may choose your own repair shop to fix your vehicle however, if your repair shop charges more than the company's suggested shop, you may have to pay the difference.

The Illinois DOI also states that there is no law that states how many estimates you must submit or that limits the number the company can ask for. Your insurance company may ask for several estimates to determine the median cost to repair your vehicle.