Yeah, those babies need a protector, and the mama is aggressive. I saw a sign in HHI along a boardwalk that was next to the street leading to the church we went to that said feeding alligators is dangerous. That sign convinced me to be very careful when I'm at HHI!
Bobbi
In the wild, alligators will usually flee humans -- even very large alligators. They don't view us as prey, and because we are taller than they are, they see us as a threat.
However, if you see one in a populated area (golf course, park, Disney World, etc), you can rest assured that some moron has fed them. Having a top-level predator with a brain the size of a walnut associate your species with food is
NOT a good thing. And yes, fed alligators will become aggressive. In fact, they will be much more aggressive than a Mom defending her babies (she will usually just hiss or bluff-charge, rarely actually attack and then only if the target is actively threatening the babies).
The general rule of thumb with alligators is to stay at least 15 feet away, regardless of size. On land, alligators are much faster than humans for a short distance, and even a little 4-footer can spoil your day with a painful bite.
At Everglades National Park, we have very large numbers of visitors and staff in close proximity with alligators every day without any problems. Alligators are just like most other wildlife -- leave them alone and they'll leave you alone.