Newpipe can also download. No need for bloated YouTube-App, Premium subscription or ti hassle with a command line tool (in case CLI's are not your thing).
As also mentioned by others, youtube-dl seems kinda dead. However there is a good fork/successor called "yt-dlp" which, in addition to other nice improvements, also somehow manages to work around the enforced heavy bandwidth limit by YT.
It's just a command-line tool to download audio/video from youtube (and many other sites). You'd need to setup the iPad thing yourself, maybe using something like Plex?
In your comment, is allowlist a list of videos only they can watch? (not a list of 'age ranges' or 'channels', but actually being able to select individual videos). I was never able to get something like this out of youtube kids when I've tried it in the past.
All these services curate for kids and I want to choose what my kids watch, so they are all failing me. (I'm with the others who go with YT premium, youtube-dl, kids watch with vlc or something on a tablet).