If I had to pick just one PS4 game for kids to recommend, it's Little Big Planet 3. It was clearly designed to be kid-friendly, although adults have loved the game, too.
It's basically an adventure-puzzle game, where you use these stringy little heroes through various levels and obstacles.
The best part is that it can be played co-op. Either you can play with your children, or they can play with each other. Can't beat that for less than $18 bucks!