I really hope you got pics of her car. Did you get any witnesses? Witnesses are a huge advantage -- especially if you have anyone that can say she was texting or not paying attention.
Find out who the owner of the car is. If the father, then go after him for sure. If you don't find out who owns the car, then suing the father could end up getting you nothing. You must sue the owner -- it might be her mother, or it could even be just a friend's car.
Things like this just leave me dumbfounded. Some people raise the stupidest, most irresponsible children. If I was that girl's father I'd have told the cops to cuff her and charge her with theft. There is no way my unlicensed teen is going to drive unless it's during driving training or a recreational off-road vehicle.
You have a point I did not consider. I assumed the father owned the car, because he said there was no insurance. Find out who owns the car. I also assume you traded info with the girl and her father, or the cop wrote it down for you. Put everybody you can on the list for the suit...all owners, the girl, her father, mother, and any body else you can think of who might be in the least bit liable. Let the judge will sort out who is liable.
I agree with you as per if I were the father...the kid would be in cuffs. It is tough getting witnesses, especially after the fact. She hit you from behind, and even you did not see her commiting the deed. You only have the results to work with.
I would take pics with my cell phone at the scene, if someone hit me. They are acceptable in court, and real good evidence. You also have the tag, a pic of the perp, and the incompetent cop. You even get the dynamics of the incident...where the cars were...skid marks...pieces and parts...etc. Always have your cell phone with camera on your person.