Turns is the best puzzle for kids on the Apple TV. It's easy enough to control, even for the smaller kids.
Turns have different categories from cool cars, to cute animals and healthy vegetables. It's free to try, so please do. If you like it, it's easy to upgrade to all the motives by a single in-app purchase. The game is professionally narrated by an American voice actor, so your kids can learn new words while playing on the big screen.