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If your 14 year old has been charged an adult fare for the cruise, I think it's likely that they will also be charged as an adult for the excursions. That was my experience on a recent cruise anyway, also with a 14 year old. Adult charges applied.
Check in the brochure or on line - but I think she is an Adult. However, you are going to the caribbean. Most, if not all, trips can be done yourself MUCH cheaper and better value as you do not need to go with other large groups and can choose the best time for you. Taxis are cheap and costs for families or groups are therefor cheap. We booked the swimming with Dolphins ON LINE before we went (Tortola). they even told us the taxi fare $4 before we went. We chose our own time, got the taxi $4 at the port, (time to dolphins place 5 mins) we and 1 other (3 in all) had a pool and dolphins to ourselves whereas the ships trip had 14 in their pools. Shore excursions are expensive on all cruise lines. If you have a family it gets extorionate. do research with the tourist boards, check out the shore excursions on offer by the ship, replicate them through tourist boards and SAVE money. Remember when you book yourself LEAVE ENOUGH TIME TO GET BACK ON THE SHIP BEFORE IT LEAVES. Times of arrival/departure from ports are in the itenery. Last but not least - buy yourself some jewellery with the savings !!