I did not watch the entire video, and missed the jacket thing. I just went back and watched that part, and agree that should have been done differently.
I think I heard you mention Clinton Anderson? And I see she flexes the pony... I would do those desensitizing things with the pony's nose partially flexed, that way if she decides to spook, you can bring her around in a one rein stop.
I also agree lessons will help further her skills, but I feel you are on the right track.
Good luck, and you'll have to post more videos of their progress together!