Sounds like it could possibly be a stifle issue. Slipping in canter (unless the footing is not so good) is usually a sign of problems in the upper leg. Most of these issues particularly in young/green/out of work horses will be alleviated when muscles in the hind quarters are significantly developed.
I had a little ottb 3 year old mare that had stifle problems and often slipped in canter, after a few months of work with her I have since sold her and she has not had a problem since.
Basically it was a matter of lots of hill work (walk and trot only - canter is just about useless as far as muscle building up hills is concerned!) and strengthening exercises under saddle. Lots of leg yielding, turns on the forehand and shoulder in to try and promote muscle development in her hindquarters.
Lunging is probably not great at this stage, as you can cause more problems working them on a small circle continuously if they have leg/joint damage already. If you do need to lunge, do it in an arena and walk up and down the arena so that there are lots of straight lines in the lunge 'circle'.
Weight is another thing to consider, if your horse is a little 'light on' in the weight department, the ligaments in her stifles are not overly well supported so more likely to 'slip out' of the patella. If this is what is happening with your mare, make sure she's a good healthy weight, nice and round with good covering over her ribs. My mare wasn't a big eater and was very light on as she'd just come down off the track, so I ended up having to give her Vitamin B12 injections to stimulate her appetite.