That's exactly what a friend and I (but mostly him) built. He has two kids, I think 6 and 4 now, and he's got a simple website accessible in his Lan that has kids stuff grouped by show with big thumbnails. It's remembering what has already been watched, and last we talked about it he wanted to limit watchtime per day. I mostly built the crude parent interface where you create new categories and paste links to pages you wanna scrape with youtube-dl. He's planning to put it on github eventually after removing all the hard coded stuff...