Normally I agree with taking an older car to an independent shop.
But in this case, I’d agree with getting it to a dealer. I believe a Mini is a BMW underneath, and local independent shops might not want to or be able to work on it. The fact that the Advance Auto couldn’t scan the codes tells me it’s not a typical one they see. I also agree with having the car towed, just to be safe.
Good luck, and I hope the fix isn’t too expensive.