This is a hard one for me. As a gymnast, I experienced coaches who said inappropriate/ineffective/down right mean things to me which have greatly affected the way I see myself to this day. They really wore me down and suck a lot out of me. However, as a coach, I am tough and have high expectations for my girls, meaning that I am not always well liked by my kids, especially when the asst. coaches are present who are much more lenient and "fun." I am not demanding of these girls because I want to be mean or think it's fun to beat them down (and I hope I'm not beating them down), but because I see their potential and want them to work up to it. There are times I will call kids out for misbehavior, not working to potential, or cheating because those are things that I am not okay with as a coach. I try not to make an example of a kid or humiliate them in front of others, but talking to the group as a whole or personal chats in the middle of a rotation don't always seem to do the trick, so sometimes I'll need to say something out loud where other girls can hear. But, I also try to offer praise for hard work or trying to make corrections so it's not all negative.
So it's tricky. Have you watched any of the practices to get a sense for yourself of what is going on? Or talked to any other parents? I don't mean gossiping, but asking in discrete ways how other girls feel about how practices are going to gauge whether this is a common problem or one more specific to your child.
I don't think walking out the door is the answer, as there are lots of sides to every story, but I also don't think you should minimize what your daughter is saying. It's tricky. Perhaps start drafting a list of some definitive examples of things that have happened, not only how the coach reacted, but also anything that lead up to it. This could maybe show some patterns and help get a better picture of what is going on- if there are things your daughter can do differently and a means to gauge whether these are just personality conflicts or valid concerns for your daughter's well-being.
I hope things resolve themselves and your daughter can continue doing what she loves!