I didn't see any lameness, FWIW, though certainly have your trainer not only watch the video but have her out to evaluate her in person.
I wouldn't say that she is using her back here. What she is doing is stretching into the contact, which comes first. *Once you are certain she is sound*,
you can spiral her in at trot, then send her out and forward... you will see lots of stretch--its a leg yield of sorts on the longe. You can do it at trot and canter if she is willing, but be careful about keeping the circle as large as you can to start with, and when you ask her to come in, do not ask for too small a circle for too long - watch the tracking of her hind legs on the circle. When her hind legs make a larger circle than the front (haunches out), she is working HARD and must be released back to the large circle after just a few steps to a circle or two. Its a lovely gymnastic exercise, done in brief segments, and you should see that trot get more stretchy and lofty. Just be careful not to ask for too much--I only longe a sound horse for about 10 min. Per side, and I try to keep the circle as large as I can, walking a lot, unless I am working on an exercise.
She is super cute! I hope her comeback continues without any glitches