OK let me see what I can add.
From having the brief opportunity to see said network myself, and trying to help her myself on a few occasions, it appears to be just two computers connected via a cross over cable. Both have Windows XP and have ICS enabled
Her source of internet is a EDGE or GPRS phone connected to computer via bluetooth. The primary computer has the bluetooth connection and (correct me if i am wrong, Kiya) she uses the wifi adapter with the secondary computer
she using a nintendo wifi USB adapter, which from my reading, is a re-branded Buffalo USB adapter. It seems to work fine with her Wii as she is able to update it.
As for her Nintendo DS, she can connect to it but she is unable to connect to other players.
MY reading on the issue on nintendo's website implies that she simply needs a faster internet connection (DSL or better). She only has AVG antivirus and the Windows firewall and she manually opened the required ports for the DS to work but still no dice
Hope this helps