I'm the family cruise editor here at CruiseMates.com. I recently wrote an article which is on the main menu of articles when you first log onto CruiseMates.com which gives general tips on what to do with kids while in port. Here are more details:
St. Thomas: Yes, take a taxi to Magen's Bay. You'll save a bundle and it's a great beach for families. Also, upon your return, have the taxi drop you off at Paradise Point Tramway in town. It's a short, fun ride with great views of the harbor from up top. (You may want to get a throw away camera for your child.) It's then a 10 minute walk back to the port from there.
St. Martin: Ask the shore excursions desk for suggestions of beaches you can reach by taxi that have bathroom facilities. We went to one years ago (Orient Beach) which was very lovely but part of it is a nude beach. Now that my daughter is older, I don't think we'll take her there on our St. Martin call next month since the regular beach is in close proximity to the nude beach and I think she'll feel comfortable. I can give you more suggestions after we call there at the end of April on our Disney Cruise. Why don't you post this message again with my name on it in the beginning of May and I'll give you more suggestions?
Smooth sailing!
Luisa Frey Gaynor