The simplest solution would be:
NTL Cable -> Cable router (new) -> Vaio and Daughters PC (one cable each)
As it seems you use a cable modem currently, my experience is of the set top box situation and not necessarily the same. But with my system I set it up on the Ethernet (not USB cable as you have).
Then I had to copy my pc's MAC address and put this into the router's configuration (then NTl still thought it was talking to my PC and not a router)
Unless you get a better answer, I would suggest re-configuring the internet connection using an ethernet cable to your vaio from the existing modem. Once that is working, find out your Vaio's MAC address and enter it into the router's identity. Then setup your system as shown above.
Hope this helps!