What happens if you give her a longer rein?
My mare used to do this a lot, only in groups, especially if others in the group were going faster than her, she would do this dumb little jiggy trot thing and try to yank the reins out of my hands. I would give her more rein and she would take off. At the time, this behavior made me nervous, so I tensed up and held on too much.
Relax, let go, put leg on. Easier said than done, right? This wouldn't work for drill team, but on a trail ride, try leg yielding side to side, serpentine, shoulder-ins to get her attention back on you. When you give her a long rein and she walks out quietly, praise her profusely.
My mare and I go all over now, and I mostly trail ride on her on the buckle if we are at the walk (I still trot and canter on contact, she is an eventer/dressage horse). And stay super relaxed in the saddle, it helps her so much.