I agree the boyfriend doesn't need to be there. A reasonable manager should take your word for it. Do it in person, not over the phone. Bringing in your boyfriend as your boyfriend weakens your stance as a paying customer, male or female.
However, there is value in having the boyfriend there to say "if you don't fix this you will lose 2 customers." Be sure he doesn't say or demonstrate any flexed male muscles and ego.
And both of you should say that you will be sure the word is passed along to all friends that there is a mechanic there whose behavior cannot be trusted outside the store.
So what if he is a besotted idiot and how would anyone know if he does this to other women unless the manager is notified? I'd sure be questioning whether battery has occurred.
Frends know gud humors when dey is hear it. ~ Da Crockydiles of ZZE.