Two ethernet ports to bridge two different networks

I have no desire for a network router. I have one box with this arduino in it and connected via network cable I have an other box with a different arduino in it. We'll call the network bridge arduino one, and the other arduino two. In the first box next to arduino one is a relay that I am controlling from the arduino. The second box has an other relay next to the second arduino. I need to close both relays remotely and that is it. So if I send a message to arduino one saying "Close relay 1" it will close the relay. If I send a message to arduino one to "Close relay 2" it will pass that message along to arduino two. All of my messages are 16bytes in length and every message is processed before the next message is received since I have a 1Hz message rate. I will never come close to meeting the SRAM max of the arduino. The code for this is extremely simple if I could figure out how to access the second network port on the arduino, there has to be a way to setup an arduino on multiple different networks.