As Sunny said, I most definitely would NOT be worrying about any form of rein change in canter if she is not balanced in it. Flying changes will add to the confusion and you will have one very stressed and nervous horse on your hands.
I would be cantering her on the lunge, on a large circle, and sending her forward in canter. It sounds like she is 'trantering' - trotting behind and cantering in front. Often this can be because she's not forward enough. If you really drive her on, in most cases it is near impossible for the horse to 'tranter'.
Under saddle, canter only on a large circle (20m or wider) and on straight lines, with only shallow corners, rather than trying to ride her into corners. Get off her back, put your leg on and 'choof' her up, just about gallop her a couple of times around the ring, then start to come back down onto her back, slow the canter back to a controllable and comfortable speed - but diligently maintaining the forwardness in the pace, and bring her onto a large circle.
Basically you want her super sharp off your leg, so when she does go to 'tranter', you can put your leg on and she'll go and get back to a true canter.
Forward is the key ;)
Once she's forward, off your leg and cantering true, with the canter a little faster than what you'd usually work a novice horse at, then you can start steadying the canter, shifting her weight onto her hind legs and riding deeper corners.