Cross-canter is the proper term for the gait that is commonly called "cross-firing" or "disunited." It refers to when a horse is cantering on one lead in front and the other lead in back. As opposed to the correct lead, which is when both front and hind inside legs lead. The cross-canter feels very rough and is awkward for both horse and rider.
The problem you describe with your horse could be a balance issue but it could also be caused by a back problem or other unsoundess. I would suggest you get her checked out by a vet and/or equine chiropractor. If she has a problem with her back or hips, it could be inhibiting her ability to canter correctly.
If a physical problem were ruled out, I would start working her a lot on haunches-in and leg-yielding (two tracking) to develop her strength and coordination in her hips. Once she does well with haunch control, go back to canter and try to keep her haunches-in while she canters. The horse pushes off into the canter stride with the outside hind leg. By keeping her haunches bent slightly to the inside, it keeps more weight on the outside hind so that she has to push off with that leg and so she maintains the correct lead.
You should work on haunches-in at the walk and trot until you can keep her bent with her haunches-in in both directions. Once you are ready to start cantering again, only canter short lengths so that she can maintain the proper stride. Gradually increase the number of strides you ask for as she develops strength to sustain the gait.
Incidentally, I do not like to canter young horses in the round pen or on the longe line (mounted or unmounted), because they do not have sufficient balance to maintain a proper canter stride in that small a circle, and they invariably cross-canter. If they are allowed to go on and on, you end up conditioning the horse in an impure gait.
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