On BT Passthrough mode (assuming you're using a real Wii BT Adapter), you only have to sync your Wiimotes with the sync button on the battery cover once (make sure a Wii game is running, though, you can't sync otherwise). After this initial syncing, it behaves like on a real console, you just need to press any button on the Wiimote while a game is running and it'll will reconnect automatically. I have no idea of what is causing your other issues, though...
Avell A70 MOB: Core i7-11800H, GeForce RTX 3060, 16 GB DDR4-3200, Windows 11 (Insider Preview)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)
