Well, from what I understood, these two different setups works fine, but you can't get it to work properly together, right? So, you could try using two separate BT adapters, so you could use one for setting up wiimotes with Dolphin and Toshiba Stack and the other for the rest, but it's not guaranteed to work...
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)