Does Mario Kart have any kind of network setup that you can do, or is everything supposed to be automatic? It would theoretically be a lot easier to diagnose the connection if both instances of Dolphin were set to use static IP and you could tell one game to connect specifically to the IP address of the other game, rather than just letting the game search for other GameCubes and hoping for the best.
When you set up the TAP, did you configure the network bridge to use the same settings that your Local Area Connection adapter used to have before you added the bridge? Once you add the bridge it becomes impossible to configure the original adapters, so you have to configure the bridge instead.
When you set up the TAP, did you configure the network bridge to use the same settings that your Local Area Connection adapter used to have before you added the bridge? Once you add the bridge it becomes impossible to configure the original adapters, so you have to configure the bridge instead.