Hit By An Insured Vehicle, Driven By An Unlicensed Driver (ga)

I was rear-ended and the other driver was found at fault. I have the police report and photos of the accident. The vehicle the other driver was driving was his mother-in-law's and was insured. However, the driver only had an international (Mexican) drivers license that isn't valid. Their insurance is denying coverage on the grounds that he wasn't authorized to operate the vehicle.

That seems fishy to me - he had permission to drive his mother in law's car. Do I have any recourse? I'd rather not file a claim through my uninsured motorist coverage because my rates would go up. Would I need to sue the other driver