Thank you for your question. I'm sorry to hear about your situation.
Because you lowered your insurance so that it only covers liability, your insurance company is not responsible at all for any damage to your car and is not responsible in helping you in this situation. They are only responsible for helping you with claims for payment from the other driver when you damage or injure them and you are at fault.
That being said, if the other driver was at fault for the wreck, then they are responsible for all your damages. This includes the storage fees for while your car was at the tow yard if the car was in a condition where it could not be moved.\
The first thing you need to do reject the offer to settle. Tell the insurance adjuster that they are not providing you enough money and that you will not accept it unless they also cover the storage amount.
The next thing you need to do is have a mechanic look at the car and give you an estimate on how much it will be to repair the car. You can then send this to the insurance company along with the bill for the tow yard and demand payment.
If they do not pay, then you have to sue the driver. You can sue for up to $7500 in California small claims
courts. All you will have to do after filing suit is go to court and provide testimony
to show that the other driver is at fault.
When you sue, provide a copy of the lawsuit to the other driver's insurance. That may cause them to increase their settlement offer to provide you with enough money so that you will drop the suit.
Please let me know if you have any other questions.