Dolphin emulator: Skyward Sword won't pass the "Connect motion plus" screen
In the controller set-up screen, there is a checkbox labelled "Attach MotionPlus", if this is unchecked, your emulated controller will not be recognised as having MotionPlus capabilities.
Additionally, the Dolphin Emulator Wiki says that versions of Dolphin prior to 5.0-10056, released 4 months and 3 weeks ago (May 3rd), were not capable of emulating the Wii MotionPlus. It is very possible that you were using a version which did not have this functionality, as in your own words if your version "wasn't the most recent, then it was at most a month or two old".