Legal Question in Personal Injury in California

You can sue the other party for all the damages you suffered but your insurance company is entitled to be reimbursed for expenses that it paid. If your insurance policy does not cover rental car expense, you can sue for that and not have to give any part of the award to your insurance carrier. But if someone does not have any insurance it suggests they probably have very little or nothing in assets so you will not be able to collect on the judgment you get.

Double check that your own insurance policy does not cover the loss of use or your vehicle, espeically when the other car is uninsured.