It sounds like either a soundness issue or a fitness issue. Most horses, once they are fit will not cross canter.
You may wish to wait until the horse is 3yrs old before proceeding under saddle. The horse is probably still rump high, and physically may not be mature enough to canter correctly.
Don't even bother cantering. Trot hills and cavaletti poles to build up muscle... If that doesn't help, than this is a physical problem.
I had a mare just like you describe. Even at 2 she did not canter right. She is 10 now, and it is very clear that it is a physical problem. I've had 2 vets look at her, X rays, flexions and a full workup. No one can figure out the problem. X rays are normal, tried joint injections, and pentosan yet she is clearly off in the hind end. Her trot looks fine. The last vet thinks the problem is in her pelvis.
A traumatic birth can also cause pelvis issues.
However, given what you describe I would be very concerned this is a soundness issue. Does the horse ever canter normally in the field?
Some lameness issues only appear at the canter, contrary to popular belief. It is true the majority of lameness issues show at the trot, but rarely (especially pelvis or back issues), it will show up at the canter.
At this point I would consider a full lameness evaluation with flexions. Especially if this mare does not canter normally while in the field. If she does a lot of bucking/cross cantering, and fails to hold her lead out in the field, I would be very suspicious of something being wrong in her hind end.
It is not natural to cross canter as a foal...
My mare was also vet checked and the vet missed it during her pre- purchase exam. Most vets are not trained to look for lameness at the canter. Another issue is that most people see bucking/cross cantering as a young horse or attitude problem, and not as a lameness issue.
You can also practice cantering on the lunge. I find it easier to do a small circle, than as you push the horse out to the larger circle, ask for the canter pick up. You want the horse to bend to the outside, as it makes it easier to pick up the correct lead. IF they are bending to the inside, it is very difficult to pick up the correct lead.
This goes for under saddle too. Bend to the outside, move hip to the inside as you ask for the canter.