What can you do if the other driver's insurance company is low-balling the value of your car?

You have rights, unfortunately you have to prove that your car is worth more than what they are offering. Low miles, clean interior and exterior are sure ways to raise the value of the vehicle. If the vehicle was a pig sty the value just dropped a bunch. It also helps if you have receipts for any repair work that was recently done and paid for. You don't have to accept the offer, you can negotiate for more money but keep in mind the appearance of your vehicle.