The unfortunate thing about a lot of these alligator zoos are that the animals in them have usually been picked up by animal control after stupid people start feeding them, causing the alligator to lose its fear of people. Once that happens it will start viewing human contact as sources of food, and it can't integrate back into nature. That's when your pets and children get attacked.
Alligators are generally not aggressive with things it knows are too big for it so long as you don't fuck with it. When down in Florida understand that there are gators in every single body of fresh water. Let them do their thing, and they won't come near you.