Auto insurance question - body shop selection?

My car was hit while parked. I made a claim against the person who caused the accident. The insurance company has sent me an estimator who wrote a report. The ins company sent me a check for cost of repairs (according to the estimator). The problem is that the estimate is on the low side. We both have Gieco... show more My car was hit while parked. I made a claim against the person who caused the accident. The insurance company has sent me an estimator who wrote a report. The ins company sent me a check for cost of repairs (according to the estimator).
The problem is that the estimate is on the low side. We both have Gieco insurance. I also have collision coverage.

My question is as follows:
Should I go to a body shop that is linked to the ins company, or should I pick an independent shop to do the repairs?.
Thanks
Update: Note:
The car can not be driven, it has to be towed.
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