You've raised several additional questions/issues:
1. Would the dealer have insurance on the car and be liable to fix it?
Dealers have insurance on the cars on their lot that covers those vehicles while the cars are owned by them. Without checking the dealership policy directly it's hard to know for sure, but it's likely that the dealer insurance coverage expires automatically when the dealer no longer owns the vehicle. It wouldn't hurt to check with the dealership, just in case.
2. Under most insurance policies you have the right to select which body shop does the work.
3. If you are able to locate the driver of the other vehicle, even if they don't have insurance, it's still possible to go after them for damages if you win a case against them. Once you have a judgment entered in a case against them you can garnish wages, go after assets like bank accounts, and even go after personal property. If you can't do this yourself there are collections firms and attorneys who collect judgments on contingency. It may take a while and you won't collect everything you're owed after the legal fees, but it won't cost anything up front and it's one option to recoup some of the costs.
4. California doesn't have a two-day grace period on buying a new car. The "cooling off" period is available for used vehicles under $40,000 and must be offered as an option which you can purchase when you sign your contract.
That option would not, however, allow you to return a damaged car.
5. The lender can require you to have specific coverage but wouldn't generally be responsible to you if that coverage wasn't adequate to meet their requirements after they made a copy of your insurance card.
6. If the dealership is unable to fix the car, your insurance company would be legally obligated to replace it. The insurance company can also chose to replace the car when it would be more costly for them to have it repaired than replaced.
7. The insurance company is unfortunately within their rights to deny coverage. When you purchase a new vehicle, your old insurance policy automatically transfers to your new car, typically for 14-30 days.
But because you no longer had comprehensive or collision insurance
on your older vehicle, the only coverage that would have transferred to your new car would have been your liability coverage.
If you'd been at fault, your liability insurance would have covered you for personal injury
or property damage to another person.
I know this is not the answer you were looking for, and I'm sorry that you've been put in this position by the other driver.
My recommendation would be to pursue a judgment against the other driver. Even if it's just in small claims court you can still sue for up to $7,500 and then go after them to repay you.
It may take a while, but if they have a job and you can locate them, it may be worthwhile to pursue it.