Parents should have an allowlist of devices to be able to join their network. And then they can require root certs or something for access outside of a narrow allow list. There's a host of ways to solve both problems. Just remember to check for hardware keyloggers on your (the parents') devices, as kids could use them or try evil maid attacks, etc. if they feel totally encaged.

This will only work in practice if one of the parents is a network technician. :-)