You can have the teacher's computer work as the proxy, but to do that correctly the teacher's computer is probably not running Windoze.

You could create a little script that the teacher runs that sends a SIGHUP to squid, which should close all of the connections. If that doesn't do it, a kill and restart would definitely do the job. I don't know if squid can keep state across a HUP. But, we were looking for a fairly easy to implement solution, so I'm assuming that means no script writing and no dicking around with 'sudo' and things like that. Installing OpenBSD and getting squid to work is actually pretty easy.