YSK you can still play videos meant for kids on a mini-player-like mini-screen ANYWAY despite YouTube's restrictions on mini-playing kids' videos! I'll illustrate how you can!
Why YSK: So that you'll have the ability to play ALL videos on a mini-window similar to YouTube's MiniPlayer, even the ones made for kids that are restricted from being played on the usual mini-player.
Done on an Android 16 phone: Samsung Galaxy Z Fold 5. YMMV. Unsure whether the same tactic will work on an Apple iOS iPhone or iPad screen.
Click on the YouTube icon and press "Open in Pop-Up View" to have the video play like a mini-player anyway.