Legal Question in Civil Litigation in California

Re: Who is responsible for my rental car?

Probably, but only to the extent your rental was reasonably necessary. In other words, if the repairs should take three days you can't keep the car for a week; you also can't rent a Rolls-Royce.

Whether her father's insurance company decides she is covered will not affect whether she is liable, though it may very well affect whether she is able to pay any judgment you might receive.

Btw, it's not "obvious" that she is at fault. I can imagine several circumstances under which she wouldn't be, and even some under which you would. You're probably right, but might not be depending upon the facts.

Re: Who is responsible for my rental car?

Yes. In this type of property damage case the person who hit your car would be responsible for all reasonable costs incurred by you as a result of her negligence.

As far as the car insurance being in her father's name... I would be very surprised if the coverage did not include her. But that is her, and her father's problem, she is responsible for the damage to your car regardless. Your own insurance should also cover the vehicle damage itself.

That being said, insurance coverage can be a tricky thing for a lay person and insurance claims adjusters are not always upfront with you. If this is not resolved in the near future you may need to contact an attorney.