You probably have 2 things going on:
1) Your dad's proxy server isn't forwarding enough ports for the Wii
2) The delay caused by routing everything through the proxy server is causing lag
#1 is solvable. #2 probably not. Both are up to your dad, though. You need to take this up with him.
For more info...
Go to: www.nintendo.com
Click on: Support
Click on: Connecting to the Internet (Getting Online)