This one is tough for me as I don't have any experience building software for kids. But I do have lots of UX experience, so I would probably approach it similarly: start off with a prototype, going with my gut on UX decisions. From there, have some kids use it with as little direction as possible and watch their behavior. What do they click on? Where does their mouse move to? Where do they get confused? What's missing?
It's definitely useful to have them provide feedback as well, but I imagine it's like UX for adults in that often people say one thing but do another. Just keep it in mind and correlate with others too.
There are also data collection laws regarding kids. To be honest, because kids software feels like a whole different realm to me I'd probably bring in someone else to help me, or at the very least do a ton of research into existing studies and observations of others.