And on formal night, polo shirts are not okay - even for children.
I happen to disagree about the jeans issue, but amaretto is correct, they are not expressly forbidden in the dining room and you will see them. I don't happen to think jeans are particularly appropriate for a really nice restaurant (think china, nice silver, linen tablecloths, waiters in fairly formal attire) at home, so why should they be at sea?
I think babies can wear anything they want!
Not to mention, it's just too doggone HOT in the Caribbean for jeans if you ask me!
You and your sons will have a wonderful time, no matter how you are dressed, however.