I once had a parent that had a L6 "text" clinic every sunday at her house until I found out about it- REALLY! It was early in the year so we were concentrating on skills rather than routines at that point. I found out quickly, because my gymnasts always have a look with the dance and they didnt look that way.
Know it alls are tough, its her way of trying to stay in control (IMHO!) I would say somethng like "I appreciate the feedback. Maybe you'd be more comfortable back at your old gym," etc or "i appreciate you feedback, but lets leave the coaching to the professionals" Slightly polite, but it should keep her quiet- for a few weeks at least! If she doesnt get it, I would have the HC or owner call her in, ask her if she is happy and supportive of your program, and if so, to keep her coaching opinions to herself, if not not perhaps its time to hop somewhere else.