That's because the OP didn't claim that the coach was hitting her child. I don't think the coach is. But I take exception with your attitude to let a coach do what the coach thinks needs to be done. Parents need to be involved to protect their kids from all adults in authority....coaches, volunteers, teachers. If all coaches were always well-behaved toward gymnasts...well, we wouldn't need that little list on the USAG website, would we? And just to be clear, I'm not saying that the OP's coach is a predator. Just using the list as an example that there are coaches who would take advantage of this idea that parents shouldn't be looking over their shoulder.
Nothing dramatic about claiming that continued anger and harsh words cause damage to little kids. The OP is looking to prevent such a thing, as a good parent should! This coach is using harsh enough language with a SEVEN YEAR OLD that the child is crying for an extended period of time and I assume this is happening frequently enough to concern the parent.
Like Bog said, if you wouldn't allow a teacher to speak to your child this way, why should you allow a coach?
OP, it is a hard call to make. And a lot might depend on your and the child's relationship with the coach. My DD can handle a little harsher coaching language from her main coach then she can a coach who comes in once a week because there is an extended relationship built on time and trust built up across the coach/gymnast/parent triad.