I finally got around to reading the document that penseur2 told me about, and I got it working! Thanks!
To answer adam_boz question/concern, it's not the switch that matters, is the IPs associated with each of the two NICs that I have in my Linux box. I had to insure that those ips were in two distinct networks, i.e., that the 3 first bytes of each ip were different. In my case, 192.168.0.x and 10.10.10.x. Then, I had to insure that the internal IP for the 192.168.0.x gateway (a windows box) was in that same range, and that the internal IP for the 10.10.10.x gateway (a router for a wireless modem) was also in this other ip range. This provides two distinct networks, even though all cables are connected to the same switch.
After that, it was a piece of cake to implement the routing tables and rules.
Thanks a bunch.