Personally speaking, if one of my employee's bad mouthed another to a customer I'd be PISSED. That's not the customers job to hear about internal crap...HOWEVER!!!!! I don't work with Aholes and anything bad said in front of a customer would be something I, as a manager' would have addressed PRIOR to it getting to the point of venting to the clientel.
That being said, I assume you work full time? Regardless...do you REALLY want to be MISERABLE that many hours a week? You arent' responsible for your mom's situation. GET OUT!! How long are you going to put up with feeling lousey? Someone else suggested that you AND your mom both get out, which I agree with. However, it might not be as easy for her to make a horizontal move (find a management position elsewhere). You on the other hand should have no problem finding another position with compitent management. I bet most restaurants would KILL for someone with 6 years experience. Hit the papers and look for another job NOW. Nothing is going to get better and will most likely get worse where you are now.