I can't put together your description with what I see in the video, which looks like a very quiet pleasant horse. I'm not sure if you know, but you clucked to her, which is a signal to get moving and keep moving in the round pen. She trotted along just as you told her to.
That said, videos can be deceiving, but again...you said she works very well for the trainer. So it's a real puzzle. But neither do I see a ton of evidence that she really is afraid of you. I'd really need to see how she acts when you are handling her. Just because she doesn't run up to you and jump into your lap, that doesn't mean anything.
Is it possible that you're used to draft horses, and the little extra pizazz the Friesian adds seems a lot to you? Or that you haven't been around a lot of young horses?
Maybe you're doing something that scares her? In the case of trotting in the round pen, maybe you didn't realize that you told her to, and she was just doing what you told her to do.
Maybe something happened with you and her in the past? Young horses can be very impressionable, but they never just randomly take a disliking to someone 'just because'.
Too, if young horses are out a lot, and not worked with every single day, they can get skittish. Especially on some people's farms, there's not much noise or activity, just a quiet field. If not worked with every single day, basically, they get very herdbound and nervous when away from the herd. It takes so much work to 'make' a young horse. Some will tolerate less interaction than others - for some, it's really critical that they have tons of interaction of all kinds.
Maybe that's what's happened, because typically, a Friesian-Draft cross usually isn't a very nervous or tense animal. Quite the contrary. Even a purebred Friesian is not commonly a very shy or tense animal, again, quite the opposite.
As far as conformation, she has a type of conformation often seen in Friesian draft crosses - it often creates a heavier animal than the Friesian, with an overall sturdy build.
She would be particularly suitable for driving, if she can continue to do so well in training. As a riding horse, she might appeal to someone who wants a quiet, but pretty horse. I wouldn't think she would be a super jumper, but she might do well at lower levels of dressage, many horses do.