Sue The Driver Or Owner Of Car?

I was in a car accident in Louisiana where the other party (22) was at fault. The car she was driving was owned by her parents and she was exempted from their insurance, meaning the insurance will not cover the expenses. The damages she caused have devalued my car significantly and she is not willing to pay for the damages caused. I would like to take the family to small claims court. However, given the driver's age, I am worried the court will not enforce her to pay. Am I able to sue her parents under the family care doctrine and/or negligent entrustment laws or does that not apply in this situation? Most lawyers will not take my case given there is no personal injury so I am trying to do this myself but would not want to waste money suing the wrong party. Any advice is greatly appreciated!!