Change your passcode, change your Apple ID password, enable two-factor authentication, and update passwords associated with your password-recovery path; security questions and email addresses associated with account recovery. In this case, a trusted recovery telephone number (for two-factor authentication) may be a problem, too. Though you will know if your Apple ID password changes.
Treat this for what it is. A breach.
A breach where you have some limited authority over the perpetrator too, in this particular case.
And to be blunt, I expect the kids to win these efforts long-term, until and unless the parents substantially improve security.
Parental controls seemingly exist to teach the kids the limits of their parents and educators, and about the limits of the parents’ and educators’ technical skills, and about the worst inclinations of parents’ and educators’ personalities. Any kid that’s inclined can bypass these controls and access the ‘net, too—kids are curious, persistent, observant, clever, and they communicate. Kids are usually particularly good at shoulder surfing parental passcodes, too.
Some of the following won’t apply here, but much of this will:
If you think your Apple ID has been compromised - Apple Support