The registered owner of the car is now reporting the vehicle as stolen, however the driver involved in the accident is a friend of the owner, was partying with the owner on the evening of the accident, and the DA is not pressing charges for an auto theft because the two parties knew each other and the car was not taken under force.
The registered owner's insurance company is denying our claim for our property damage.
What recourse do we have?

Contact your home owners insurance carrier. That's why we have insurance. They not only should take care of repairs, but sue the their insurance Co. for reciprocation. Your insurance Company has lawyers that are specialists in all phases of suits due to damages. Don't hire an attorney of your own, you would lose money and it's not necessary. Let the pros handle it for you.

Be sure they include the fact you porbably had to stay at a motel during repairs.

Was that the one in Sacramento,Ca. where you guys weren't home and the car went all the way thru the house ?

call your home insuracance and have them talk to their insurace.

Your brother was driving. He is responsible for dealing with it. If it was on a public place, including a car park the usual driving rules apply, the fact that he was provisional, and uninsured may well put a bias on the case. However if the other driver did a reverse T-bone into your car it is down to them regardless. You might want to consider a small claims action first ie get the first strike in. If the police were not involved at the scene then it is very unlikely that they would take any interest now. If the worst comes you will have to sblit the cost of a bumper with your brother and pay for your own door. Just make sure you aren't taken for a ride by their insurers as they will inflate the costs something rotten