Sine the baby too young, you cannot leave the baby in the daycare center onboard the ship. They do have a play center for kids under 3. You can also sign up the kid for splash academy (obviously the parent has to be present).
In Bermuda, I suggest buying the multi-day bus pass and look up things to do in the island. The bus pass will allow you to explore the island on your own time and your own pace.
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