My wife was rear-ened while stopped to make a left turn. What rights does she have?

The accident happened Nov. 25. She filled a claim with the at fault drivers insurance and notified ours as well, but everything was going through his. They accepted fault before the police report was submitted. She was not injured but did go to the hosiptal a few days later to get checked out. The adjuster''s reports stated there was $11,000 in damage to the car. We were notified today that the driver was only insured for $5000 so that is all that they will pay, even though the car is worth more than that, $12,000. Also they terminated the rental car because of this. We notified our insurance company about what is happening. Do we have any legal rights to go after the driver?