How to limit my kids to playing on my own server or each-other's worlds?
Solution 1:
Minecraft doesn't provide in-game options for that. Why can't you firewall the router?
TBH minecraft servers don't really have nsfw content. The worst you can find is at most some mild or obscure swears, as Microsoft did implement a swear filter. Most illegal acts, e.g. pedos finding children, scamming etc are quickly reported as long as they are going on the advertised servers or some other big ones. They have to face these things anyways when they are older, why not educate them about scams earlier?