We have done a few cruises and stopped at the same places with a child and I would recommend the following:-
Tortola - Worth taking the ferry to Virgin Gorda - either yourself on the ferry or on one of the organised tours. This is a wonderful place, a little walking involved to get to the actual beach area but well worth it! Tortola is only a small place if not so you could just get off the cruise ship on one off the "safari style trucks" available at the quayside and take a trip to the beach. These go backwards and forwards all day.
St Martin - The best thing to do here is shop, shop, shop!!!
St Kitts - Again, I would take an organised tour and go to Nevis - you take a catamaran trip, some snorkelling, a barbecue style lunch on the beach and plenty of time to go for a wander or spend time on the beach. If you want to go around St Kitts I would probably just take a taxi from the quayside - they will show you all the highlights and you can choose how long you want to be.
Guadeloupe - We ended up here on a Sunday - everything was closed! This was a beach day for us - but a very good beach day!
Barbados - There is so much to do, you have to come back for a holiday to appreciate it all! We first came on a cruise ship 15 years ago, and have been back every year for the last nine! With the children, I would recommend the Harrisons Caves - this would take a couple of hours - a quick tour shows you most of the island and there are some great places to stop for lunch!
From experience the children really don't want to leave the ship - they are so busy with activities etc you have to tear them away! Enjoy your trip!