Can I sue an auto repair shop for causing additional damage to my new vehicle?

Question Details:

I took my car to an auto repair shop that was selected by my insurance company. A few days later the company called me and said the vehicle was ready. I arrived to the shop and noticed a dent on the back door that was not there. They took responsibility for the damage. In addition to that the original repairs were sloppy. They kept the car for another 2 days. Today I went back to the shop and noticed that the door they damaged had signs of being fixed and dented. Now the keyless system doesn't work. What can I do?

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