Can I take the tire shop to small claims court? Do I have a case?

On 8/24/15, I took my car to get the tires changed. Upon my return an hour later, I found out that my car was involved in an accident. Even though my car was in the shop lot, an employee took the car (before doing a tire change) a 1/4 mile down the road where he was hit as he was trying to do a u-turn on the 2-way avenue. The shop did not collect any information from the tow company and I had to ask the officer on scene for a case number. The tire shop promptly got me to a rental car and said they would take care of it.

The next day I got a call from the appraiser attempting to schedule an appointment to see the car at my residence. I didn't know where my car was. I called both the tire shop and their claims department to ask where my car was and both directed me to contact the police department. Why? I wasn't responsible for the accident. I eventually located my car. I'm sure this is only the beginning of a very unreasonable tire company.

My car may be totaled and their claims made it very clear that they will only pay what's necessary. I made a request over the phone with their claims department for additional compensation for damaging my car and wasted time doing THEIR job. I was denied. The handling of this entire situation is extremely poor.

Location: America's Tires
My car: 2006 Honda Civic SI (80k miles)

Can I bring this to small claims? If so, when and what parties should be involved?

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