Fear is tricky. Your daughter is lucky to have the trainer help her overcome and conquer her fears (as well as a great mom!) My first horse I ever rode proved to be more bronc than broke and it was many years before I regained the courage to even attempt riding again. I looked around for a really well reputed riding arena (they even specialized in helping people overcome their fears) and once I realized I could put my trust in my equine friend, I started to feel a lot better. My instructor has been phenomenal in helping me as well and knew exactly how to help me progress.
Now, I am far more confident on a horse and handle things a lot better if they act up and I've learned a lot. Getting bucked off or unloaded can be very scary, especially at a young age but trust your trainer. Things will improve! I know when I had an issue with one of the lesson horses that was a bit too much, my trainer just moved me to a slightly less difficult horse and now I ride the original one without issue!