Not sure why everyone is trying to up sell you and not answer your question. NC would not be my dream vacation, but with kids workable.

You didn't say the age of the kids, but at NC, you have the pool and a bar just a few steps away, a great beach for kids (not a great adult beach). There are food options, good grocery all a short walk away. Much cheaper than chartering a boat and depending on the kids age the expense of a crewed boat is wasted. With a car rental on site you can rent a car as needed or take a taxi. When we kept our boat there, pre Irma there was a great collection of kid friendly cats (meow cats) around.

Now to toss that wrench in, look at an All inclusive in Cancun with kids, they all have kids clubs, pools, food and beach (some good, some suck). Much cheaper than BVI. When we were running a charter boat in BVI with our young daughter this was our "vacation" spot and she was much happier there than BVI. She loved all the kid activities and being away from us....and us away from her for a few hours.