The other insurance company should not be deciding what they "say" is the maximum amount covered and this is the be all end all, but they should pay as much as needed within the law and state legal limits to make you "whole"..
- Ronny I guess in your world the OP should be totally covered regardless of the amount the other driver was insured for, unfortunatly this is the real world. If the other driver is only insured for $5,000 that is ALL their insurance company is required to pay. Could they pay more..sure, will they...I think it is safe to say NO. But then again neither would any other insurance company.
If the Maximum amount meant nothing then EVERYONE would just insure their vehicles for the State minimums and be done with it. Unfortunatly for the OP and the Dad, the State minimum in CA is only $5,000 for Property Damage.
Now, this does not mean that the OP can not go after the other driver for the difference. But getting a judgement is only one part. If the other party has no means to pay the $10,000 it would be a victory in name only. Although I guess the OP could frame the judgment saying that they won..but that won't fix the car.
One thing the OP may want to also try is to file a small claims case. The limit is $7,500 but since there are not any lawyers involved it would cost around $100(or less) to file the suit. Again, it may still end up a victory in name only. But you may get lucky and be able to find their job or a bank account.
This also does not mean that the OP should not go through the Dad's policy with a fine tooth comb to verify that they are in fact not covered. However, if you live at the same residence and are not on his policy you may be specifically "excluded" and may be one of the reasons they would not cover you.
As for the $200,000 minimum that someone mentioned. That post came from CA(Canada) and not CA(California), and perhaps Canada has a higher requirement.