>>> whenever the printer is switched on and plugged
>>> into any of the laptops, the internet
>>> connection on the router drops out
Does it make any difference whether you "plug in" first or "switch on" first? Pure speculation, but I would suspect an electrical 'spike' of some sort is killing the ADSL signal, so that the router needs to be rebooted to regain it.
Is the printer located close to the router? If so, moving it some distance away might resolve the issue. Also, try using a different USB cable as worn contacts might be contributing to the problem.