Well even though you run thru a router your external IP address is the same for both PC's. That is the actual line provided by your ISP. That can only be changed by them. So when you connect to a tournament it logs your external IP address. Not the one your computer was assigned by the router.
So i highly doubt that both will be able to connect to the same tounament as both your IP's will be the same. Your external is what is detected. go to grc.com and try the shields up
test. I can guarentee that from either PC it will show the same IP address. That is cause of the IP is the external one it detects.