PharmaNAC is a NAC supplement that I've read a lot of research on.. a lot of doctors and scientists trust it because the NAC shouldn't be exposed to air because if it becomes oxidized it is unstable and ineffective, but these tablets specifically are individually wrapped and carefully manufactured so that this doesn't happen.
In one study done at Stanford they gave PharmaNAC to CF patients and it decreased their sputum activity, the neutrophil burden in the airways, and airway inflammation with no side effects. I'm not sure if the subjects were children (probably not) but it seems like maybe this NAC formulation would be a good one to try if you've been experiencing side effects with other ones. I use it, it dissolves in water and is effervescent (kind of like alka-seltzer) and tastes pretty good too!
I found some of the research on their website which I think is just www.pharmanac.com. Hope this helps!