You do have an actual claim here. Diminished value. I argued this successfully against a New York insurer. There are several kinds of diminished value. Shoddy workmanship, inferior material, and the fact that your car is worth less because it now has an accident history. If the car is repaired and the repair is satifactory, you can still claim diminished value because your car now has a significant accident history (any good dealership will be able to tell your car has been repaired even if it is a very good repair).
Take your car to a dealership. Have the dealerhip tell you what the car is worth. If they tell you what the car is worth less because it was in an accident, ask them to put it in writing. Present this to the dealership and tell them you want to be compensated.
I had a three year old Honda CR-V that was rear-ended. I successfully argued diminished value and was compensated several thousand dollars in excess of repair costs.
When a car is new and it has been in an accident, the value is diminished quite a bit. A car that is older's value is less affected by accident damage (everybody expects a 10 year old car to have been in at least one accident). If you plan to keep your car a long time the diminished value will affect you less.
