I got my daughter a surface book with Archlinux on it when she turned four. She'd previously been using an ipad so I wanted something that had a touchscreen, and I installed KDE as the desktop. She learned how to use it extremely quickly, and has even started in on the commandline now that she's 5 and knows how to read. GCompris is great too.
Me and my wife haven't bothered with parental controls and instead just keep an eye on her usage, but I agree with other commenters that controlling things at the router level seems like a better bet.
You should put your foot down and tell them it's all about free software while they're under your roof; they can push open source once they're 18 and have their own place.
Linux for Kids?
I'm thinking about building a desktop with one of my kids and I would really prefer to put Linux on it. My wife is not a fan of the idea, however....