According to the Commissioner of Insurance for Louisiana you can decide which body shop does the actual repairs to your vehicle.

The LA Commissioner's consumer site for auto insurers also notes that an insurance company’s payment will normally be based on the lowest of three estimates. So if you chose the body shop that does the repair but their estimate was the highest you may need to negotiate with the insurance company to pay this amount above what the lowest estimate was for the repairs.

The insurance regulator for Louisiana notes that anyone with insurance related questions or concerns is invited to contact the Louisiana Department of Insurance at 1-800-259-5300 or 225-342-5900 in Baton Rouge or write Department of Insurance, P.O. Box 94214, Baton Rouge, LA 70804-9214.