If you are going to get one, I would recommend that you find one that has the "anti-burst system"... This will make your work on the ball much safer. It has an inner membrane that quickly "seals" incase the ball is puntured, making the ball deflate slowly rather than bursting and causing you a paralyzing injury.
I don't know about the peanut shaped balls. Frankly, I haven't really been on a ball in a while. I will continue to use them for pressing motions mainly because a bench "impinges" my shoulders a bit, and for some abs too. I would just stick with plain ol' round balls personally.
Your kids are pretty close in age to mine. My kids love them, and roll all over the place on them (crazy kids!). I don't think this is necessarily dangerous unless they are attempting to do exercises with weights like they see you doing (very bad idea). It is just adding to the wide variety of movements that are so essential in those formative years. Lefty - who posts in here - has a 9 yr old boy who can balance really well on a ball. Lefty is just trying to groom someone who can beat me at my own game!
55cm seems to be the best, all-around size for a ball, even if you are a little on the tall side. Check
www.swissball.com (not sure if that link is still active) and you should find a variety to choose from.