Hotels and condotels with pools on Ambergris, listed more or less from north to south (may have missed one or two):
Gaz Cooper's Playa Blanca, Avalon, SunDiver, Journey's End, Essene Way, Captain Morgan's, White Sands Cove, El Pescador, Belizean Shores, Seven Seas, Blue Tang Inn, Paradise Villas, AquaMarina Suites, SunBreeze, The Palms, Ramon's Village, Belize Yacht Club, Hideaway, Exotic Caye, Xanadu, Villas at Banyan Bay, Tropica, Banana Beach (two pools), Mata Rocks, Royal Palm Villas, Victoria House, Caribe Island Resort and Sunset Beach Resort. Also, Cayo Espanto (splash pools) and Caye Chapel Golf Resort.
P.S. Why don't you post some info on your hotel on Caulker -- we've heard several good reports about it.