While my hunch is that it's okay to zap young children, just to be on the cautious side, I would try to inquire with others more knowledgable AND who will likely reply to you within a few days. The biggest reason why I would hesitate is that especially the three year old may not be best able to communicate to you quickly how well the zapper is or isn't working. Two sources that I'm confident will reply to you:
As for the latter, I've been using their zappers for well over a year. If you inquire of them, tell them "pittsburgh drew sent me" and they'll likely know who you mean.