Your kids will have a blast, and you will, too! We took 3 boys, ages 5,11, and 15 for 2 weeks, and could have stayed longer. The most fun is seeing the BVI through your kids' eyes!
Some things to ponder:
Stay more than one day in a spot and "dig in" a bit, when it makes sense. Kids enjoy exploring, etc. Half the fun is hiking, renting a jeep, taking in dinghy around, heading in to town, visiting with people, buying food, etc. In fact, one time we dropped all three off in Great Harbour, hoping for a little quiet time. About 90 minutes later we headed back in to shore, and found they'd all found a group of same-aged island kids to play with. Now that I look back on it.....not our brightest parenting move, but we thought they'd stay together. Nope, within a short time, the little one was playing some kind of hopscotch with some locals his age, the middle one was playing soccer, I think, again, with kids his age, and the oldest was playing basketball. This was over 20 years ago, and it was a more trusting time, but they're all culturally sensitive, confident adults, who love to travel and experience new things so maybe that was ok. When we were there many years back there weren't a lot of kids with cruising couples. Now, with catamarans, there seem to be a lot more families with kids along than when we sailed a number of years ago. I'm sure yours will find new friends wherever they go!
Some other things: establish some basic rules, guidelines and routines, adjusting as you go. You probably sail often wherever you are, so this won't be new. I remember our youngest had some short "time outs" for misbehavior. I think he had to sit in the head for a few minutes a couple of times, although we discussed putting him in the dinghy with the garbage (He's still quite a character.)

I think Leverick Bay is a great place to reprovision, as they have the kinds of foods my family loves to eat. Good selections, reasonably priced, etc. Also, bring plenty of snacks and such that your kids like so you can save a bit there. We had 3 boys who were always hungry (still are), so we brought things like granola bars and other easy to pack snacks, like Salted Nut Rolls and Pringles that could make it on the plane. It can be a challenge to feed kids. I remember one time during the trip, we sent them on their own to the restaurant near our marina in Nanny Cay, and followed them a bit later (keep in mind one was 15, so that made it easier to send them alone). They had headed back to the boat by then. We ordered pineapple with our breakfast and were told, "We don't have any left. These three young boys were here, and they kept ordering pineapple until it was all gone." But, those are the kinds of wonderful memories you'll cherish long after the trip ends. Have a great time!!