they also have a private island at labedee? and does that mean we should not book an excursion for that day, but instead go to the beach party?
Labadee is actually a small peninsula on the northern coast of Haiti that RCI owns, so it isn't an island although it is private. You have no choice if the ship stops at either Labadee or Coco Cay. If you want to leave the ship then you go to the private island (or peninsula). There is no access to private tours or places outside the control of the cruise line.
Check out this thread
to see a map of Labadee and a google earth photo of the facility.