Personal opinion on kids and low carb:

I low carb at 30 grams of carb per day. I'm a diabetic and I'm overweight.
My two girls (ages 8 and 9) also low carb, but at a much higher carb level than I do; between 100 and 125 grams of carb per day mostly from fruit, whole milk, yogurt, whole grain breads and veggies. They're young and active, still growing and neither of them is overweight. They do get the occasional high carb treat; part of learning to make healthy choices for life isn't NEVER eating anything that's high carb, it's learning that those foods feed the tastebuds only and not the body and should be kept to the occasional treat. It's my personal opinion that young children (defined as under the age of 12) should not have their carb intake restricted to induction or near induction levels and I believe that Dr. Atkins agreed on that point: he didn't recommend very low carb for children under the age of 12 and suggested that simply cutting junk food and highly processed carbohydrate foods from the diet and replacing them with healthier choices would be a good start for younger children:
http://atkins.com/Archive/2002/1/5-51665.html
I'm trying to teach them that food is fuel; not entertainment, a security blanket or the "fix" for a bad day or some other emotional hurt and that the purpose for food is to nourish our bodies...BUT...there is a time and a place for "fun" foods as well.