My kids are more on maintainance levels of low carb at this point and I don't "limit" milk per se. They usually have some with breakfast, lunch and dinner, but not huge glasses...more like 6 ounces each. In between meals they can have water or Kool-aid made with Splenda...I usually steer them towards water and they're gradually getting the idea that water is what you drink when you're thirsty (not pop, Kool-Aid or milk). They also eat yogurt, cheese and broccoli so they are getting plenty of calcium from those sources as well.
I don't think it's necessary to put growing children on induction levels of carbs. In fact, I really wouldn't recommend it. Since kids generally are more active, are still growing and usually have higher metabolisms than adults, most would probably lose well on maintainance levels of low carb.
I'm in the position at the moment of trying to keep my oldest (almost 9) from losing any more weight. Between our changing eating habits and her starting Concerta (a timed release version of Ritalin) last January, she's gone from 90 pounds down to 71 pounds since then and her pediatrician is having a fit! 19 pounds is a lot for an 8 year old to lose in 6 months and she's seriously concerned that it is going to start affecting her growth. This is a factor for all kids who are still growing; you don't want them to lose too quickly or it could affect their growth. That's probably why Dr. Atkins didn't recommend strict low carb for children under the age of 12. Since the Concerta kills her appetite and I can't get her to eat more, I'm having to try to make whatever she eats count both calorie-wise and nutrition wise; full-fat yogurt, full-fat sugar-free ice cream (homemade), higher fat meats and cheeses, and a higher (not high!) level of carbs from fruits, veggies and whole grains. I could get her to gain weight again quickly by letting her go back to eating junk food, but I'm not willing to go there.
Be careful with trying to get children under the age of 12 to lose weight; slower is far better in those cases (like maybe a few pounds a month!). What my pediatrician was actually recommending even when my daughter was 15 pounds overweight was to try and hold her weight where it was while her height caught up, not having her lose (growth issues again).