I agree with Nopie...

I only have two kids, but I've gradually been weaning them off the high carb junk food and steering them towards more fruit, veggies, yogurt, cheese and sometimes nuts as snacks. When I first started low carbing, I continued to cook as I always had with a meat, veggie and potato, rice or noodles as a side dish. I ate the meat and veggie and left the rest for everyone else.
It helps that both of my girls love fruit and veggies, but that sweet tooth is hard to tame. For that, I've just switched to sugar-free products (jello, ice cream and pudding) and started making their kool-aid with Splenda instead of sugar (they never even noticed a difference). In the long run, giving your kids less sugar and junk food can only be a good thing and you will be teaching them good eating habits that will last them a lifetime.