What happens if we press charges against a 16-year old boy who was not authorized to drive our car?

First of all, you place your self in potential criminal liability by knowingly making a false police report. Do not do it; making the false claim does not mean the insurance company will necessarily believe you instead of speaking to the young boy, who they will contact to see if he can pay for the damages or has his own coverage. Check your insurance policy exclusion of coverage language to see whether infrequent usage by a non-household driver is covered but since he may not have had a license and even if he did he could not drive without an adult in the car, so that probably automatically voids any coverage. Ask his to pay for the damages. If your daughter is a minor, what was she doing with your car? Read her the riot act.