Once I agree to an estimate, do I have to have my car fixed, and do I have to have it fixed where the insurance company tells me?
No. The responsible party has a duty to pay you for the damage done, but you do not have a duty to fix your vehicle after you receive fair compensation – you may use the money as you wish.
If you would like to use a body shop of your choice, you are free to do so. The insurance company cannot require you to use a particular person or shop.