You can sue the repair shop in small claims court for damages up to $5,000.00. If you go to trial, you will need a mechanic or representative from one of the dealers to act as an expert witness for you. They will probably charge you for this service. The mechanic will have to testify that, after examining your car, the work you were charged for by the repair shop was not done.
You can sue but you need an expert witness. How do you know the two authorized dealers didn't mislead you to get the business.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 577-9797 or via email at Eric@RothsteinLawNY.com. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. The above answer is for informational purposes only and not meant as legal advice.