Two network addresses

I am running a Squid proxy server for my company (30 users)and have all the users setup with static IP addresses 192.168.1.xxx with a subnet of 255.255.255.0. These are working fine. I have two NIC’s installed, one for the network and one for the cable modem. My problem is getting two of the systems, which have to be set at a different ip address of 172.21.22.xxx with a subnet of 255.255.255.186, to find the proxy server. I can’t change these ip’s at all because they connect to a router that must be used to connect to one of our suppliers. I need help in detail since I am new to Linux and also have never worked with two different addresses.