I'm after the collective wisdom of the BA FT crew

Sat on 200k BA miles and 241, looking for destination for myself, wife and 11yr daughter next summer. We normally go to the USA each year, and have covered the typical places like Florida, DC, New York, West coast (top to bottom), Vegas, Yosemite, Yellowstone, and Hawaii.

However, we have never been to the Caribbean, and quite fancy the idea as a change. We are not "sit on the beach for 2 weeks", "put the kid in kids club for 2 weeks and we get drunk", or "I want to be waited on". We like variety on a holiday, getting out of the hotel by car to visit sights, bit of beach, bit of activities, nice food, good pool area, friendly & clean hotel, and some shopping. For example, this year we are starting in Miami, heading down the Keys, up to Fort Lauderdale, over to Disney (on property), and then finish with a few nights on the Gulf coast.

Quite like the idea of an All Inclusive, especially if we may be limited to expensive food choices in a hotel. We also prefer Hilton if possible due to the Diamond status.

I know summer may not be the best time to go, so are any island less likely to be affected by poor weather?

Can anyone suggest an island and/or hotel that is served by BA that could fit the bill? As a fall back, connecting via Miami might be an option but have found this harder to get redemption. Availability for the Caribbean appears much easier, for example there is still availability for this summer showing.

Thanks all