It's the parent's job to make sure the child has enough confidence and self-worth not to be put down by anyone else, be it the school bully, a coach, a teacher, etc. My kids have been in competitive situations since they were 6 or so years old, and neither took it personally when the coach got emotional. They have been known to laugh at the person getting upset, actually, which doesn't always go over too well either. My younger daughter tells me she likes it when her dance instructor yells at her, it means she's trying to push her to become a better dancer, and that she sees potential there for improvement. I must point out that both of my daughters have an extremely high level of self confidence.
About the "skating like a baby" - doesn't that put an image in your head about how the skater was skating? Comparing her to the beginner skaters? She would know how she looked, so much more than a list of 'get your back up, extend your free leg, do this, don't do that', as long as she knew the difference between a beginner and a more experienced skater. When I skated, I had that image in my head, of the beginner adults, and our awkward, stiff posture. I'd try to channel an image of Michelle Kwan, to get that glide, the arch in the back, the shoulder and arm position that was so much more pleasant. Whenever my coach would try to correct me with a list of dos and don'ts, I'd forget what I was even working on.