When we were there last it was this exact time of year and we had the same issue. Honestly, our only good beach days were at Flash of Beauty on Anegada and at Fischer's Cove. So maybe take the ferry over to Anegada for a day! The lobster roti at Flash of Beauty is one of the best things I've ever eaten in a long life of really good food. And for our rainy days we did a lot of day drinking, so maybe not family-friendly, but go to Leverick or Top of the Baths where there are pools and it'll be fine.