Hello, welcome to the forum. What kind of adapter are you talking about? Do you have a UK Wii this time or a US version? Why not just get a UK Wii?
As far as the remote thing goes, if this is currently your only problem, try unplugging your Wii from the wall for a time and plug it back in to reset the hardware...you can also try this with the batteries in the remotes. This really shouldn't be happening with new hardware. Is the hardware new? Are the remotes new?