I don't know if getting a switch will work, because I don't think there is a DHCP server on the WAN side, so both routers would fight over the ip address.
But you can plug your broadband in to your first router's WAN port and then plug the second router in from a extra port from router 1 in to the WAN port on router 2. This will make it so you have internet on all of the network but no one can see each other if the are on different routers. As well as let you have different DHCP assigned IP addresses and more security on router 2's network, because not only are they behind router 2's firewall but they are behind router's 1 firewall as well.
This is kinda what I was thinking I needed to do, how will this setup affect internet speeds on both? Thanks!
I didn't think about that before I asked, the speed that is.