When you setup YouTube kids app, it has an option to allow only the shared/whitelisted/curated content. Don't remember the exact terminology.

Then from your main account, go to a channel, click three dots -> Share with children -> Share. Can do the same with a single video too.

It can be a painful process though. If you want to unshare, you have to find that video and repeat the process. Or unshare it in the youtube kids android app by logging in as a parent first.

Would have been nice if i could share a play list. That way I would only have to modify that play list to add/remove a video.