It should not be difficult to make a whitelist only client, meaning you do not see anything unless it is from a whitelisted npub. A bit more tricky is to give only parents control over changing the whitelist. So like a dual app for parents, which has an access to the whitelist and can modify it.
Discussion
But at the same time, why bother. They will quickly figure out that they can access all of nostr from any other client. Every phone has a web browser.
Yes, basically an app for parents or some NIP that let an npub to control another npubs following list for example may work.
About finding out stuff in other clients, it's mostly something related to the parents and how they manage to keep them safe from the bigger internet space!
For us, it's important to give this safety control to parents, not government and KYC.