Please don't take this the wrong way because truly I don't mean to sound rude; but the bar moving so much is a real potential hazard! She may be hooking over the bar in a protective tuck response to it hitching as she goes around. Thats also the kind of response that turns into a learned behavior that her coach will have to work through even though the bar at the gym is perfectly safe.
I'll share a drill I use at the gym, but please don't try it at home before speaking to her coach! Even if the bar is secure, the floor and the mats at the gym make it the safest place to drill or do skills with an apparatus. If the drill sounds good to you, I'd recommend asking the gymnasts coach if she could try it at the gym. If all goes well and you have the mats for it at home, then I still would ask her coach if it's ok to try at home before proceeding.
The drill I use in the gym is this: take a preschool bar, lower it so the gymnasts bottom leg is just off the mat, or ball of the foot on the mat.
Position the bar facing a wall, and have the gymnast cut a leg over the top as if about to do the mill circle. Have them press up and then try to 'reach' for the wall with the top leg. I usually place the bar in a way that allows them to get their foot against the wall (with a straight leg only) so they feel stable in the full stride position.
Their chest should be up, shoulders down, and they should feel the bar pressing slightly on the mid thigh of their bottom leg as they reach. I have them do the drill until they know the feel of the correct amount of pressure on their bottom leg, which they can use as a signal that their stride is good and they're ready to commence the skill.
Doing that has helped some slightly more wary gymnasts who were nervous with the chest up, open stride position right before committing to a very fast skill. It has a very free-fall feeling to it that takes some getting used to with some gymnasts.
(to be very clear about the drill, I always start it so that the gymnasts bottom foot is in contact with the mat, and the top foot can reach the wall. Only with straight legs of course. As they get more comfortable in their stride, I gradually raise the bar so that the bottom foot eventually comes off the mat entirely. After that I back the bar away from the wall, but at that point I still stand there to spot if needed. I do this drill ideally before they've ever attempted the full skill.)