When should I get rid of the queen of spades in Hearts?
There is no etiquette required when playing the QS.  It is worth half of the available points in the hand.  Anyone expecting you to be "polite" with it (whatever that means) is unrealistic and should go back to playing against the computer.  

There are strategic exceptions.  For example, it may be advantageous to pass on an opportunity to play the Queen if you are trying to stick a specific opponent with it and think you can do so safely later in the round.

That being said, are you sure they are actually upset?  Maybe they are trying to trash-talk or joke about their misfortune and just not doing a very good job of it.