If you have a distinct wireless router appliance (and are not using your desktop+wireless card as an ad-hoc router) then you should be able to set up your network to work independently of your desktop. It is possible your network is configured to use the desktop as a DHCP server so when your wife's connects, it tries to contact the desktop to obtain an IP address. The wireless router should be capable of acting as a DHCP server itself, and should probably be configured that way before you add a Mac to the mix.
That's kinda like Spanish to me. I understand the words, but don't know what all of them mean.
What is the make and model of your wireless router?
Now
that I can understand: It's a Netgear WGR614 v5.
just plug them into the router,
One's a wireless connection. Actually, if I buy a mac it'll be a laptop, and they'll both be wireless connections.