Don't mess with the Wiimote and don't try to pair it with your system. That will prevent Dolphin from seeing/using it, or worse, Dolphin will see it, but it will conflict.
Unpair your Wiimote, just make sure Bluetooth is enabled, Continuous Scanning is enabled, you have a real Wiimote configured, then just press 1+2 and it should connect.
Unpair your Wiimote, just make sure Bluetooth is enabled, Continuous Scanning is enabled, you have a real Wiimote configured, then just press 1+2 and it should connect.