The Cunard Queens have precedence in the Red Hook Terminal. If one of them is in the same time as Princess, Princess has to go to the terminal in Manhattan. Sometimes scheduals get screwed up because of storms and extra sea days. Normally Princess will use Red Hook in Brooklyn but it is not guaranteed.
When you get or print out your boarding pass it will tell you which terminal you are leaving from in NY. I just printed mine for the May 17th sailing of the Caribbean Princess and we are leaving from Brooklyn.