Well I am no expert, you really want someone like Kerrelli to answer but I have experienced this problem and found that constant transitions on that rein helped improve balance. And it goes without saying nowadays that back, saddle and teeth have to be checked first!
I have also found that in the small school that I am able to use, my mare has a particular dislike to cantering in - she almost panics and has to career around! but if I hire the local indoor school (huge!) or have a lesson with an instructor she is fine.
I also school out on a hack on the moors and again we seem to get a different reaction to cantering! I use the gorse bushes and hawthorn trees for markers and she is much more relaxed about it - perhaps a change of scenery might take her mind off being awkward on one rein.
I school in my field ATM, but there is a livery yard next door to my field that hire the sandschool out for a fiver! Sorry I have pressed a button on my laptop and my pound sign has stopped working yet again!! I dont know which buttons I have to press to un do it!
LOL - that's nothing, my daughter, whilst doing homework this evening, managed to make the whole screen upside down!! - Luckily I have a computer literate son who was able to rectify the problem!
Hi, make sure you are supporting him with your outside rein and inside leg. Exercises like leg yielding in and out on a circle can help with falling in as they will put the horse back onto your outside rein. Think about your position as well, as it is easy once the horse starts to lean, to lean with them, therefore encouraging