It looks to me like she has a very comfortable trot. I don't know much about hunters, but she looks very nice to me. It would definitely be worth a try. It looked to me like she was bulging her shoulders some. Of course I was not there so I can't know exactly what you were trying to do with her, but it looked like she was resistant to having her shoulders follow where you were wanting her to go (I can especially see this in the first video). It is never too early to start asking her to turn off the outside rein and get her to lead with her shoulder. This will help limber up her neck and shoulders and makes for more precise control of where her feet will go. You can do this in a small circle (10 or 15 meters or so) starting at the walk and eventually working up to the trot. Tip her nose to the outside but guide her with the inside rein through the circle, use your outside leg to get her to move her shoulders around the circle. It is hard for me to explain in words. I can demonstrate it in the saddle much better. This is a precursor to teaching the horse to ride shoulder in. Of course, you might already know all this. That is just the number one thing I noticed.
Good Luck with her!
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