A couple of things.
1. Hopefully this will help you.
2. Don't waste your money on Norton. In my experience, it seems to be too well-known; within a few months every major virus will have been written with the goal of evading Norton in mind. If you want to get a higher-end virus program, McAfee is good. And it's a wise idea to get one or two lesser-known programs, as well.
3. It's hard to say whether that connection will put the second computer at a greater risk. The only way to know would be to look at the trojan itself to see how it works, and I can't really do that. To be safe, it may be wise to disconnect one or both from the router until you get the problem solved.
I hope this helps. Good luck in ditching the trojan!