bad coaching
I coached at arguably the best gym in the U.S. for a few years. I can tell you that there was none of this. It sounds like your coaches are inexperience and misguided in coaching technique. The coach clearly doesn't know how to fix the problem, so he/she figures that yelling and bullying will make him/her look in control and in charge.
Whenever we had this sort of problem at my gym, the kid would back up. Line on the floor, floor beam, low beam with mats, etc. No, this fear thing didn't happen a lot (just the way the gym was), but when it did, there was no browbeating. It was simple. Go back to basics and work your way back up. No drama, no yelling. In fairness, if the child wasn't able to make progress in a reasonable amount of time, or if she would refuse to do the progressions, then a lot of times the kid would no longer be considered coachable and a decision would need to be made.
However, there was certainly a positive effort to help the athlete work through her fears.
I think the conversation you need to have with the coach would run along these lines:
You are bullying my child and it needs to stop immediately.
If you don't know how to help her overcome her fears, please just say so and we'll move on.
If you are no longer interested in coaching my child, just say so and we'll move on.
If the coach says that she DOES want to keep your daughter, your response could be:
I will assume that you believe what you are doing has been for the benefit of my child. However, she and I do not see it that way. Because I now know you want to help her, I will tell you what needs to happen if we are to stay at your gym. You will not yell at, bully, or belittle my child. You will help her with reasonable progressions, and give her time to work through the problem. If you get to a point where you are no longer interested in coaching her, please come to me and say so. In the meantime, I expect that she will be treated with kindness and respect.
And there you have it. I fully expect that your coach is frustrated and doesn't know how to fix the issue. In my experience, these are the coaches who bully and yell.
Good luck!