Not sure how to make this work...Please help!

Here is my situation:

I have two computers (both running XP Pro) that are both connecting to my router wirelessly (802.11g). I also have a crossover cable connecting these two PC's to each other. What I want to do is have them both connect to the internet independantly via the router, and at the same time be able to transfer files back and forth via the crossover cable. I cannot get this to work and I'm not even sure if it can be done. I can only seem to get the crossover cable to work if I bridge the wireless and LAN connections on computer A. But when I do that, computer B wants to use computer A's internet connection rather than its own wireless connection. But if I remove the bridge on computer A, I get limited or no connectivity on the LAN for both computers and they connect to each other wirelessly (which I don't want). Is there a way to make this work and if so, how? Thanks.