Personally, I think anyone who wants to learn to ride should learn how to handle a horse from the ground first. I know it must be hard with kids who just want to get up and go, but I think they should learn how to be around horses first and understand their nature and behaviour. There's so much more to riding than getting on the horse's back.
There's a book called "Think like a pony" - can't remember the author, but it's natural horsemanship written for children.
I cringe when I think back to my first riding lessons (and some of the later ones) - kick to go, pull to stop, pull right and pull left to turn.
There's a much better way and it's easier to do it from the start than unlearning what you've already been taught. You may be able to find a natural horsemanship instructor in your area who can help.