I currently have a Billion router set in Pure Bridged LLC so I can dial up and separate local and international with RouteSentry. Is there any way I can connect to the internet via my Wii as well?
No you cannot as far as I know, the Wii looks for an internet connection on the router.
If you looking to a once off update then its a temperory switch, but ya its gonna be a pain if you want to be online via the Wii all the time & use bridge via your pc.
You can set up a proxy on your PC, and let the Wii connect to that. I did this, but it's not a very complex setup, so while I could update my firmware, I couldn't connect to the shopping channel