Not sure if this is too late and you have been already, but we recently chartered in the BVI for a week with our three boys, 9, 7 and 5.
What we found was that it was important to limit the sailing. Get up, leave about 9 and be moored at the next stop by lunch time. This was pretty easy with how close the islands are together. Once moored, we'd swim, explore, snorkel etc all afternoon.
Second tip for sanity was something to play movies. A sad slave to the screen I know, but when we were tending the sails, we had to have something to occupy the kids. We opted for a 9" DVD player ($110 from Best Buy).
Third, get them involved in route planning. We researched all about the islands and I pretty much let them decide the route. All the islands are so close together that it didn't really matter where we ended up.
Last, pirates. The area is dripping with history about pirates. Treasure Island is based their, Captain Blackbeard and Dead Mans Cay (yo ho ho and a bottle of rum!) are all here. The weeks leading up we read loads of books and watch the odd Captain Jack Sparrow movie or three