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!
BR Krzysztof