Your kids would probably have a blast with the horseback riding. Down here, in tourist areas you usually get smallish, "bombproof", comfortably paced horses which like someone posted, can be considered as "automatic". They follow the leader and do their job. I have my own horse and am part of a riding group and we're always looking for ex-tourist horses for the kids.
ATVs? Wouldn't recommend them either unless they're riding with an experienced adult. Even then it's a touch and go subject.
Enjoy!!