A wireless router is the best solution to your problems. Linksys makes good ones, and it will allow you to have your PC and 360 online at the same time as well as your mother's laptop and any future devices you plan to purchase.
I suggest getting a draft n router for future compatibility.
Something like this will do the job nicely.
Make sure you read up on wireless security. You want to set up WPA and turn off SSID broadcasting at a minimum. You can also use MAC filtering if you're really paranoid, but I prefer not having to add a new entry to the table every time a friend comes over.