OK. My first question is do u have a router? Because it sounds like one only can have one computer connected at a time. A router would allow both computers to connect at the same time. Since you have a laptop you might want to get a wireless router.
Since you have Ubuntu installed on one of your computers it is really easy to install WINE all that you need to do is open a terminal window. Next type this at the prompt:
will@running:~$ sudo apt-get install wine
[sudo] password for will:
Then it will ask you for your sudo password then it will go about installing WINE.
Reading package lists... Done
Building dependency tree
Reading state information... Done
wine is already the newest version.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.
I already have WINE on my computer, but it will read the package lists first. Then build the dependency tree. Next it will read the state inforamtion, and then keep on going.
sudo apt-get install
Is one of the most important things that you can use to install programs without having to use a GUI.
SUDO stands for SUPER USER DO.
I hope this is a little bit more along the lines of what you need.