Most likelly the broadband modem has a router built in. Unless its like my wireless High Speed connection, where no modem is needed.
Just get some cat 5 cable off of new egg at hook that into you moms computer.
Some of these broadband modems also have 802.11 g or b wireless built right in.
If it does have wireless you can get a wireless card or you Mothers computer (if it doesnt already have one).
You'll have to check with you ISP for the specs on your modem.
Check out my Counter Strike:Source servers:
***THE DYNASTY***: 126.96.36.199:27015
*** GUNGAME ***: 188.8.131.52:27015
*** SOCCER ***: 184.108.40.206:27015