I am now back to the point where I have started. Both builtin and external WiFi are based on Broadcom chipset and neither works with HifiBerry DAC+ Pro. Without HifiBerry card the internal adapter did work.
I have also tried moode player with similar results.
So, in order to to actually solve it, should I buy an Edimax dongle? Seems it is readily available compared to Ralink one.