Aaargh, shame on me! Apparently I forgot to install VBox extensions and, thus, I had only USB 1.1 support available in my machine settings.
This was the root cause of the problem. It also caused some issues with another card but I found that disabling adapter under windows until Kali starts helps a lot.
Now both adapters work as hell without any tricks.
Sorry for bothering you with such stupid matters and help for great hints that were helpful to find the answer!