Following a motor vehicle accident, it is your right to have your vehicle repaired at any shop you choose.
The insurance companies will likely try to steer you to their own repair shops, but don't feel compelled to do so. Most repair shops, whether it is the one you choose or another, will typically work off the estimates that are prepared for the repairs vehicle by the insurance companies.
In fact, if there is any dispute, it is typically the repair shop people who will go nose to nose with the insurance company personnel to resolve the dispute for you.
If your car has been damaged, a repair estimate will be prepared. Indeed, you need not even get your car fixed in order to be entitled to the amount of money on the repair estimate.
Essentially, the repair estimate is a statement of the damage that the at fault driver has caused you.
You are not required to use the money to fix your vehicle. If you choose, you can simply request the insurance company for the at fault party cut you a check, you can deal with it in any way you want.
If you choose to repair your vehicle, Arizona law allows you to choose your own repair facility.