Hi, Emily!
Having just stepped off the ship, we found the Eastern Caribbean a family-friendly port of call -- no language barriers and no currency exchange. Most everything you'll want to do is close to the ports, and transportation is readily available.
In St. Maarten, you can opt for ground transportation to go into town or to the French side of the island, but we took a water taxi to the beaches on the Dutch side -- which was convenient, inexpensive ($6 round trip per person) and fun for the kids. Depending on the ages of your children, you may want to bring a stroller since it's a bit of a walk from the ship to the water taxis, and once you're in town, you'll want to stroll the streets, have lunch and maybe do some shopping, too.
In St. Thomas, there is much to do within walking distance of the ship -- which necessitates a stroller for kids under 3. We bought tickets to the
Sky Ride to Paradise Point which takes you to the top of a mountain and provides breath-taking views of the port. Then, we took an open-air taxi tour of the island. Although it was an efficient way to see much, I'm not sure that I would be comfortable with tiny ones in that taxi winding through the mountains and hills without seatbelts or car seats. If you'd like to see the island, I recommend booking a private car which can provide carseats for the little ones. You can get recommendations or book through the Port Adventures Desk when you're on board. You'll want the car to take you to the downtown shopping areas -- which is the Mecca of shopping experiences -- and to some key points such as the lookout over the Atlantic side of the island and to Magen's Bay Beach.
As far as when to arrive at the terminal, earlier is better -- it opens at 11 a.m. Have a wonderful day and a magical vacation. Bon voyage!
Andi