stop my kid signing out of their microsoft family account?

If they're signing out of Windows and into something else, the fix is on the PC rather than in Family Safety. Make sure their account is a Standard user, not an administrator (Settings > Accounts > Other users > change account type). A standard user can't add or remove accounts. Then check your own admin account has a password they don't know, and remove any old local accounts sitting on the machine they could switch to. If it's an Xbox, set a passkey under sign-in settings so they can't change anything without it. Is it Windows or an Xbox they're doing it on?