Gorgeous horse, bad rider. Rider in video could not keep anything about her own body quiet, hands were almost like stroking? The reins, she was thrown off balance and legs went flailing behind her multiple times, I can only imagine that would be extremely confusing and frustrating for that horse, and what's with the treats?
With a quiet rider that gives clear signals this horse would probably work out wonderfully. Wish you well with her, and very glad it sounds like you have a solid "team" that can help you with any issues that arise.
Barring dental and tack fitting issues, her head tossing seems more like a training issue, this rider could not hold onto the reins and somewhere along the line the horse learned tossing its head was a way to "grab" the reins back and pull them right out of this "trainers" very busy hands, unfortunately all she did was reinforce the behavior by allowing it, but it should be something that can be fixed.