Now I see that you wanted a pool and a fridge. Any of the condotels listed (Banana Beach, Mayan Princess, etc. have kitchens with fridges.) Banana Beach, Tropica and SunBreeze which I mentioned have pools. A few hotels such as The Tides have fridges in some rooms.
Hotels/condotels on Ambergris which have pools include Casa Caribe, Caye Beach Resort, Journey's End, Essene Way, Captain Morgan's, El Pesdcador, Seven Seas, Paradise Villas, Barrier Reef, SunBreeze, The Palms, Ramon's, Belize Yacht Club, Hidaway, Playador/Exotic Caye, Banyan Bay Villas, Tropica, Banana Beach, Caribe Island, Sunset Beach, and Cayo Espanto on a small island off the back side of Ambergris. May have missed one or two.