First, parents were only allowed to watch one lesson in four. Second, they were allowed to watch from the vantage of the barn, not from the ring or from any distance that would allow them to coach from the sidelines.
By the time we got to competing, the parents and I were usually on the same wavelenglth. If not, they pretty quickly found another trainer.
I was very lucky, I had a program and a location that were in demand and had a waiting list. If parents didn't want do "get with the program" I could easily replace them with someone who did.
That said, I very much like Dejavu's trainer's method, as it's subtle but to the point. My less tactful version was something on the order or "You need to listen to your parents about doing your homework, your chores and your bedtime. You need to listen to me about your riding."