Getting to Galveston from Houston has proven to be difficult... I could buy a car for what it would cost the seven of us to get to the hotel, and then over to the dock the next day by shuttle or taxi service. We're thinking we'll rent a van and leave it at the hotel for a week.
Rain -- try http://www.elitelimohouston.com/ or http://www.houston-airport-town-car.com/index.html Also, take a taxi from your hotel to the port since it's cheaper than the shuttles.