Yes you can, but I got great difficulty using the x box plug-in with the wii mote plug-in I think the keys were mapped to similar buttons so it had some conflict with acceleration etc.
What worked quite simply was the njoy plug with the wiimote plugin
To put it more simply as you requested.
Open dolphin
Click configure, Go to Plugins, Set pad plug-in to Njoy v0.3
Click configure on Wiimote Plugin, ensure connect Real Wiimote is checked
and Emulated extension as Nunchuk.
Click Button Mapping and observe which buttons on the keyboard is nunchuk control etc.
You may now play two player Mario Kart wii with keyboard/xbox pad.
What worked quite simply was the njoy plug with the wiimote plugin
To put it more simply as you requested.
Open dolphin
Click configure, Go to Plugins, Set pad plug-in to Njoy v0.3
Click configure on Wiimote Plugin, ensure connect Real Wiimote is checked
and Emulated extension as Nunchuk.
Click Button Mapping and observe which buttons on the keyboard is nunchuk control etc.
You may now play two player Mario Kart wii with keyboard/xbox pad.