He looks fantastic, what a pretty boy! Not sure what the trainers are trying to achieve in the video, looks like a great way to develop numerous bad habits and certainly not a great way to train a pony to be ridden safely by a child which he is ultimately destined for.
I would like to see him worked in a simple snaffle and by someone with a calm seat and good hands to encourage him to relax his back, neck and poll. He looks like he is just charging around and bracing himself against the pelham rather than being accepting of the bit and rider.
In all, great job in improving his condition he looks lovely!
All horses deserve, at least once in their lives, to be loved by a little girl.