In my experience I would never use a "preferred shop" again.
Do what Snowphun says. I'm not sure how well changing companies and making a claim right away is going to work for you, or if you can even do so with what sounds like serious damaged to the vehicle.
I use AAA Northern New England for insurance. Actually in a claim process now and it's been going fine. Dropping the car off Monday at the shop of my choice, I know the insurance estimate is lower but my shop said not to worry and that they will handle it.