Visiting Belize in June is a good time and based on your requirements I am leaning towards reccomending Ambergris Caye.
Belize is not really an All inclusive place, as there are so many retaurants and bars and most resorts do not offer all inclusive unless you are remotely located.
know where in Belize offers Alchohol included.
As for dive operators the top operators on the island that consistently get good reviews are Ecologic Dives and Amigos del Mar. If you are looking for a real small outfit which most likely it will be just you 3 plus a couple of others then Scuba Steve is a good option.
Feel free to check out my Guide to diving Belize at my website and if you decide to book I offer multiple packages where you can choose your dive operator and Hotel and get a 15% Discount off any package on offer.
These are the same packages adveritised all over the difference when you book through DiveBelize dot com is you get 15% Discount which is ONLY offered via the booking system located in the website.
Feel free to ask any additional questions
regards
Gaz Cooper
DIVE BELIZE The Complete Guide to Diving Belize