You could also try the Sugar Busters For Kids or Carbohydrate Addict's For Kids approach. It's not as extreme as Atkins, but still eliminates sugar and high glycemic foods for the most part.
If you're going to do this though, especially with kids the age you have, I'd really suggest getting them to buy into it instead of dictating the change. If it's not their choice, chances are that they won't stick to it, especially when they're out of your sight, and that could wind up making things worse instead of better.