Cat Doors For Kids?

Yes, cat doors. We have flies in our house because my lovely children think they were born in a barn. You see, they leave the door open. And it isn't just one door - it's the door between the house and the mudroom, where bugs congregate because they leave the back door open as well. Yes, two doors open and flies in my house. So, I spend the afternoons swatting the three or so flies that have come in during the day. And the other assorted bugs? Well, if it isn't flying then I'm not worrying about it. I figure those guys are too busy figuring out how to get out that they won't bother me (actually it's mostly flies that come in when the doors are left open).

So do they actually have cat doors for kids? I think that would fix the problem for sure. Or, the kids could just close the doors...