Truthfully, I don't see lameness in the video. What it looks like to me is a young, unbalanced horse being ridden in ground that is a bit deep and she's having some trouble finding her feet.
With a movement as subtle as that one, I would really want to lay hands on the horse, watch her move in person, and maybe even ride her before I made judgements on soundness. Some horses do just move funky and I've known 2 that you would swear were lame just from watching them at times...but they weren't, they just had a strange movement.
As for the original video
. Gotta love it when they finally realize that you aren't playing around
. Looks like you're making headway with her, she may make a nice horse yet.