Connecting 2 Office Computers To A Wireless Network Please Help!

Okay, thanks to everyone in advance for their help.

I have had a Linksys wireless cable gateway set up in my room for
about a year. It connects to broadband cable internet and it has the
Cable modem built in with a four port switch on the back and a
wireless access point built in. It has worked fine for me to hook up
my 1 desktop wired, 2 gaming systems wired, and my laptop roming all
aorund the house wirelessly. However, my father has just come to me
demanding that I share the internet connection (which I pay for) with
him in his office (a personal desktop and a company laptop)
downstairs. I dont really mind, but this does pose a problem. Im on
the third floor and hes on the 1st, so wired is not an option. At
first I tried using a pair of usb wireless interfaces. It works with
the personal desktop, but not his company laptop because it wont let
me install the drivers for the device. So, I must now move on to
ethernet (and therefore driver free interfaces. My thought is to
hook up the 2 office computers to a 5 port switch, connect that to a
Linksys Wireless Bridge and that will connect to my already exsisting
wireless network. My question is if the DHCP server function of my
cable gateway will pass over the wireless bridge to assign IP address
to the computers on the "new" wired netowrk of my dad's office with a
switch and 2 computers. Any input is greatly appreciated. Below are
the products im considering using:

I have the Linksys WCG200 Wireless Cable Gateway
Planning On Using the Linksys SD205 5 Port 10/100 Switch
Planning On Using The Linksys WET54G Wireless G Bridge

thanks