Ahh more canter/lope questions.. video included!

So, I've been on here about her crossfiring issue. She is a TWH, she is sound, had the farrier and chiropractor out. And she's fine. Buuut this is as close as correct as her lope is getting. This summer Im going to work with a gaited dressage trainer.. but I thought this video might help insight. And yes, I've had QH trainers be totally stumped by her haha.
Oh, and yes this is also how she lopes on her own or in the open, straight line..anywhere. Not just in the roundpen like this.

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Can she trot? Or does she pace?

Have you ever worked her over cavaletti? Cavaletti are hard to do while pacing, so encourage a trot. I am not sure if this is a fact, but one person I knew used cavaletti to help the horse break up the two sides of the body and then would ask for canter.
Pacing uses the body in lateral halves, while troting in diagonal halves. In the canter, the horse starts with one back foot, then has two diagonal legs form a kind of "fence" and then the horse continues "over" the fence with the front leading foot. That diagonal pairing is really important.

Yes over poles she'll trot beautifully, and she'll trot about 20% of the time on her own, not under saddle. But even from an actual trot, I get this result. :/

Oh. Well, now I am stumped.

She's just a weirdo! Haha And she stays super balanced that way too. So you can't "force" her out of it..

Is she just as unbalanced on her right lead?

If she is going in a straight line at the trot or at gait, does she travel straight or does she carry her hind end off to the right?

She looks like a horse that has pain in her left hind and refuses to bring it underneath her. Crossfiring is just easier for her. At the canter, she also looks like a horse that is carrying her hind end off to the right. It can be habit or pain.

If she does the same thing going to the right (and carries her hind end in the left lead), then it is not hurting in her left hock, stifle or hip.

Has anyone ever done flexion tests on her hind legs?

If she has no pain issues, you need to get control of her hips. You need to get her to carry her hip in toward the inside of a big circle -- first at the walk and trot (if she will trot) and finally at the canter. Crossfiring and lead problems are totally a result of a horse's hind end being in the wrong place.

I also see that she has very poor head carriage. Has anyone ever worked on getting her collected and riding her hind end up to her front end while keeping her head under control? That could also help and will be necessary for you to get any control of her hind quarters.