I recently was diagnosed with low d (actually, I have the adult form of ricketts, although I can't pronounce or spell it
I even had a broken wrist about a year ago that in hindsight was because of my low d or at least the way it broke was due to the low d) I'm on 20,000 iu a day now. I worked up to it starting at 2,000. I originally was going to take 50,000 iu a day but after doing some research my hcp and I decided with 20,000 because taking 40,000 a day for an extended amount of time has been shown to cause an overdose in adults. I've seen supplements of 50,000 iu but I think those are meant to be taken weekly. Once my number goes up I plan to take 2,000 iu to maintain, I get to retest in 2 weeks.
I think that 2,000 a day for a child is fine...I wish I had my links bookmarked but I don't...I do specifically remember reading that children given 2,000 iu a day is fine and that's why I chose to give that much my own children (8,5, and 4). My kid's doctor is aware of how much I am giving them and he wasn't concerned about it but you may want to ask your children's healthcare practitioner just to be sure.
Although, now that it's spring and we are outside constantly I think I may stop supplementing for the kids, then just start up again in the fall.