There are plenty of cabs/vans waiting at both the port and the airport. You might have to split off the group, especially if there's a lot of luggage, but they do have good sized vans there. I know they'd hold at least 8, probably 15. I know they'll be willing to accomodate, that's their bread and butter. Another option is the cruise shuttle, but honestly, I feel it's not worth it in Ft. Lauderdale, Orlando or Miami, yes. If US1 wasn't so busy, you could walk. Getting to the pier would be quite a hike, but walking to the entrance would be very doable.
If they had to split your group, someone could ride with your parents. Everyone gets dropped at the same place, so they wouldn't get lost.