welcome ! you should love your first cruise.
1) I always take the cruise-line shuttle. Can't help you on private shuttles.
2) In Nassau the pirate museum would be a hit with most kids. The tour I took also included 2 forts.
In St Thomas there are many options as well. If US national parks are your thing then a tour of St John is great. Kids should enjoy Coral World or Atlantis submarine.
3) any advice? Where to start? tips and soda aren't included. Formal nights have can't miss shows. If you think you might be prone to sea sickness, talk to your doctor about "the patch". Take Dramamine even if you aren't prone to motion sickness...it helps me get my sea legs.
PAST TRIPS= Enchanted Capri
Carnival: Inspiration, Legend, Valor, Destiny, Holiday, Triumph, Splendor, Fantasy
HAL: Maasdam twice, Statendam, Oosterdam
I took this same exact cruise in 2007. Let's see...we flew in the night before and realized the following morning that the hotel we had stayed at (close to the airport, I think it was a comfort inn or something) actually offered hotel to port transportation for the half the cost of the cruise transportation. For this reason, I always try to avoid the cruise transport when possible. So my rec would be to find a hotel that offers port transporation as well.
In Nassau, Atlantis was awesome! There is so much going on there for kids and adults. It was like $55 for a day pass (we bought it at Atlantis; not thru the cruiseline). There are indoor caverns you walk thru filled with aquatic life and artifacts, you have access to the Atlantis pools, beach, and lagoon, and you can take in the grounds. It's awesome!
In St. Thomas and St. Maarten, I did a beach day w/snorkeling and a horse ride respectively; neither of which I think you are looking for. Both places are gorgeous though.
Darn, you make me want to do this itinerary again it was just so great from the Glory to the ports...lvoed it! Very excited for you
Carnival Inspiraton, Feb 2006
Carnival Glory, Aug 2007
Carnival Liberty, Aug 2009