I'd school her for it every time she'd bite or kick, and so would my previous trainer. Nothing we did would work, though, she just never stopped.
I wonder what 'school her for it' means? I don't think Foxhunter's having a go at you, just pointing out, that if what you & your instructor were doing didn't work, it... well... didn't work. That's not at all the same as saying the pony was 'untrainable', just that it seems she needed a more effective, clear way of being trained. If nothing you do is working, then it's probably time to think about changing your approach.
And Unicorn, sounds like you've got the right idea IMO. Just got to take it gradually & consistently. Remember, speaking of the above, she needs to get as much practice with different people being effective with her & no more practice (if you can possibly avoid it) at her being 'effective' against people.