Then, we had routers and switches (some of which were hubs, but no one remembered they were not the same thing).

Now, we have routers (and no one knows what a switch or hub is). Most people refer to a simple router with a built in 4 to 8 port switch as a router, and don't know the difference. Fourdc knows the difference though.

An actual dedicated router with 3 ports (1 to each network, 1 to the modem) would do exactly what you want. Thats the entire purpose of owning a router.

The really sad thing is, even companies like Cisco are stating things incorrectly. The Cisco RV082 8-port 10/100 VPN Router - Dual WAN should actually be called Cisco RV082 8-port 10/100 Switch with VPN Router - Dual WAN (this is the same as the OP stated he has, just with the Cisco branding instead of Linksys).