You know your kids best, so individual results may vary. But I agree with what most have said, shouldn't be a problem. Disney is wonderful (pardon the boat pun) about having activities for all ages, so when you're onboard, no worries. My kids are older now, but when we started cruising they were younger and we barely saw them! We insisted on dinners and some activities together, but generally they were on their own on the ship.
Excursions are tricky things. Sure you could just go to a public beach, but the excursions are fun too. You have 2 options, Disney or non-Disney (like Viator for example). With the Disney excursions, you are walked right to your tour guide and are guaranteed that the boat will NOT leave without you if you are late getting back. We just did the 7 night SCar, and in Antigua we were the last ones back onboard. They literally pulled in the gangway behind us. But they waited.
In Aruba, I almost wish we had booked non-Disney, as Wonder was in port from 8:30am until 1:30am the next morning. Very little chance of missing the boat there!
The biggest difference (outside of the variable risks based on timeframes) is that Disney excursions are almost always more expensive. You can save a lot of money booking non-Disney, which we've done several times. Also sometimes you'll have better luck if the Disney excursion fills up quickly and you can't get in.
All that to say that you may be able to find something more reasonably priced and age appropriate for your kiddos if you look non-
DCL and are willing to plan a little more shrewdly.
One work of advise, some of the Caribbean islands (Martinique comes to mind) have European style "clothing optional" beaches. Disney is pretty good about warning you about that, but Viator is not. Caveat Emptor!
Cheers,
daedelus
