Hmmmm, it's shame your 17yo isn't 18................ then i'd recommend Willy T's (Norman Island). But only for one visit :-)
White Bay (Jost Van Dyke) on a day when the weather
is good is usually pretty busy with people of all ages, especially people over on day trips from the larger islands and Americans over for a day trip from the US virgin islands
. I've seen quite a few families there in the past, and the worst-case-scenario is that i'm wrong and you have to sit on the beach and have a cocktail to commiserate.