You know what, it's probably going to be much easier for you to just buy a new router
from NCIX or someplace similar....
Ditch the Telus router - it's going to be too complicated and it may be difficult to use with Shaw being that it's a Telus router. It may well have been designed only for xDSL - I don't know for certain because I don't have one.
To answer your questions though, yes, the router does need to be plugged into both her computer and the cable modem. It sits in between the two.
Assuming the router actually works with Shaw, and that it's wireless is OK, you would then have wireless access to the Internet.
The router is left between the cable modem and her computer. It's not moved anywhere. It has to remain connected to her computer and to the cable modem :)
In order to access the router's interface it has to be plugged into her computer and powered up. It looks like this;
Cable Modem => Router => Her Computer.
The problem, as I see it, is that the Telus router may only work with xDSL and not with a cable connection. That adds a lot of potential complexity to the issue.