Why doesnt this horse trot?

Brief：
This horse I do not own, nor lease, but my friend leases her. Her name is Mystic and were retraining her for English from Western. Shes an 8 year old .. 

This horse I do not own, nor lease, but my friend leases her. Her name is Mystic and we're retraining her for English from Western. She's an 8 year old Paint. And I need help! She won't trot! Well, at least with someone independently riding her. She'll trot with someone leading her, she'll trot on her own, she'll trot with someone on her back, and another person leading her, but she won't trot with someone independently riding her!! They thought (or still think) there's a problem with her poll or something (that's what the vet said) and so she went to the horsie chiropractor and got it realigned. But she still won't trot very much. It helped a little I think but I'm not sure. Would a different bit help? Or something? And if there's a bit to help... would said bit be legal for a Dressage show? At least a schooling show? There's a lot more but it won't fit. Just ask if you wanna know it!

I don't think the problem will be solved by using a different bit, I think you are just going to have to be very patient here. At least she will actually trot with rider when being led, this is a good start, so you know that she actually CAN trot. If all medical reason have been ruled out or fixed, then it is probably a psychological issue. It may be that she has it stuck in her head that if she trots in that particular set of circumstances then something bad will happen (pain, fear etc) - horses can have wierd fears and phobias just like us!! Firstly, I'd suggest lots of praise when she trots during lungeing, leading etc, then as she is being ridden get the person who is leading her to very, very gradually start to let the rope out a little and get a little further away. Stop while she is still trotting happily, before she has the chance to fall back to a walk or canter. Keep doing this, in the school, in the field, out on hacks, very gradually and patiently so she doesn't even realise the person leading is getting further away. After a while you could leave the clip on her bride so she still feels the weight like she is being led, but just have the person running beside her, again, you are just working very gradually. With patience, the person leading should be able to get further away until the horse learns it is ok to trot alone with just the rider on her back.