It a tricky proposition. The parents have primary responsibility for all aspects of therir child's well-being. Plus, the parent hires the coach, not the other way around. Rafael Arutunian for one has commented often about the difference between coaching in the U.S., where the parents and skaters rule the roost, with coaching in Russia. He who pays the piper ...
The ballet instructor of my sister-in-law, when she was a little girl, was renowned for being a tough cookie. Not only was she exacting on her students, but also she pulled no punches with the parents. If a girl lacked the talent to progress, Mss S told the parents bluntly, "I train ballerinas. I do not provide recreation for children. Your child does not have the potential to advance. Here are the phone numbers of three rival ballet schools. Your child will be happy at any one of them."