Or you can have the local interface and the cellular interface up at the same time, have the default route through the local interface but have a route to your preferred DNS server through cellular. Then the only traffic you have to pay for over cellular is DNS, which is very small.
Kids are clever, if one of their classmates is known to be tech-literate and (s)he's saying the school is snooping on you the amount of shadow IT will rise. Vast majority will install, but also have some other device to bypass.