Are you using ICS? Sounds to me like maybe you've only bridged the network adapters, but not actually implemented a "router". That's what ICS does, it bridges *and* routes. If the connections are only bridged, then each time one of the computers issues a DHCP request, it goes up to the ISP and grabs the one and only available public IP. That kicks off any other computer that grabbed the public IP previously. And so it goes, back and forth, each computer grabbing the public IP and throwing the other one off the Internet.
I’m curious, why not just get a standalone router? They're so inexpensive. You can grab a very basic, wireless N router for as little as $20 USD. I just can't see using a desktop/laptop for this purpose, certainly not long term. A standalone router also uses less power and therefore saves money compared to a full desktop/laptop.