Since most people have data services with their phones reading email without a cable or DSL connection isn't really much of a problem. The OP didn't indicate that the family really had any NEED for Internet but did have a NEED to restrict its use. No need to try again although you might have thought twice before writing.
How long would it take to remove the PC from a locked container? Would depend on the container. I have one locked in an enclosed support pedestal for a desk and it would take some serious damage to the desk to access the computer. Any kid of mine who destroyed something of mine to use something I had told him to not use would soon discover the benefits of living at home rather than locked up in a cell for a criminal act.
It appears that you might lack some "common sense" if you so quickly rule out suggestions without thinking them through.
I'm guessing that you think this suggestion by you epitomizes "common sense" - "she may have to spend a little more to involve someone with custom programming skills to keep her son from changing the router settings"