Do you really want my honest opinion?
Yes, get her vetted, and get a chiro or a massage therapist to look at her as well.
However what I see is a young horse who is learning that when she resists, she gets rewarded; especially in the first bareback vid with Shay on her, what happened when she hopped up and kicked out and stopped? Shay patted her, and stopped cueing her to go foward=reward for acting like an idiot.
Now in the first vids yes, there is some lameness there, which is why you need to get her checked out, but once she is cleared, you need to decide to commit to getting her to move, and move NOW when you cue. Every time she reacts the way she does, she gets stopped, and patted (atleast what I saw)...this is exactly opposite of what should be happening with a horse with sticky feet; and she is sticky way before she is asked to trot/canter...that is apparent by her lack of gumption to move foward on the lunge (just wandering about doing her own thing with no regard for her handler), and being resistent, and halty at the walk undersaddle.
Again, DO get her checked out, to make sure she is okay, but get on her tail about moving foward when she is given the clear bill of health.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."