Labadee is a private resort that pretty much is only beach. Most people wander around in their swimming attire with a t-shirt on. With the new pier there, ships can finally dock and so guests come and go to the ship all day. You can't leave the resort so there isn't a lot of exploring to do.
Changing facilities are generally not provided at either Labadee or Ocho Rios, other than ducking into a rest room if you can find one at Ocho Rios. At Labadee the ship is "right there" so you can return to it quickly.
Leaving the ship isn't tedious at ports with docks. Usually within 30 minutes of mooring they'll clear the ship and allow passengers to leave.