You definitely need a government issued ID plus your sea pass card. I usually just use my license or my Passport card. I leave my passport locked in the safe for the duration of the cruise. If you need something else, they will definitely make an announcement or post in the daily newspaper thingy.
FWIW, Caribbean weather almost always shows rain in the forecast. Most of the time it is gorgeous weather with a possible passing shower. Here's hoping that is the case for you guys!