It looks like the only insurance available to you is from the body shop. It does have a duty to keep your car in a safe place and can be held liable for negligence if it does not. You could indeed sue the shop (in small claims court for up to $10,000) if its insurance company does not want to cover the loss. You will have to prove that it was negligent in some way. I briefed this issue of a repair shop's duty to store a car safely a few years ago and would be happy to send the document to you if you wish.
Unless you have some reason to think the drunk driver has money to pay for your losses, I would not name him in your case as that will only be a distraction from your main claim against the repair shop.
I also suggest you talk to the shop's owner about simply doing the extra repair work for you for free - it would be cheaper for them and easier for you than going to court and getting a judgement .
If in a car accident with an uninsured motorist while your car in the possesssion of a body shop, there is a cause of action against the uninsured driver and potentially sue the body shop under bailment theory. Unfortunately, uninsured drivers are usually uninsured because they have no money. A cause of action against a bailor of property for failing to safeguard property has different standards for the type of bailment. Calling a local car accident or injury lawyer may get the answers you need in your state.
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You can request the DA set a restitution hearing in the drunk driving case and the Judge will order the defendant to reimburse you as a condition of his probation or sentencing. Also the body shop may very be on the hook for leaving your car outside the shop instead of in a secure area, under a bailment theory.
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