OP, lots of horses appear to be rather green and unbalanced when it comes to the canter, and sometime even to the trot. I'm pretty sure if he's unbalanced under you he's also unbalanced under your daughter, but with her weight it's harder to notice if you are not experienced.
So if he doesn't have a training under a good trainer under his belt, it's not something surprising. If you plan on working with him with the trainer (even lessons usually sufficient enough) I don't see why he can't be trained any further.
BTW, I do NOT recommend to use side reins to teach balance, especially if you don't know how to use them. Correct riding and properly muscling will help him with the balance issue - just takes time.