I'll take a stab at this. Unless these are wild animals that Disney deliberately kept on property (for example, the animals outside the Animal Kingdom resort (is that what it's called?), they would have no liability for the actions of the animals which wandered onto their property. Assume for a minute that I own a lake home in the northern Minnesota woods. I invite you up for the weekend. Everything goes great until you are mauled by a black bear that wanders onto my property. Can you sue me? Would you even *think* of suing me? No, of course not. It's a wild animal. I didn't invite it onto my property, but I can't stop it either.
The question here will be, I think, whether the situation Disney created (having movie night, setting up an attractive beach area inviting play on the beach area) an enhanced risk of damage by the wild animals in the area and whether they are adequately warned their guests of that risk. I'm not a big fan of lawsuits in general, but this is one where I think there would a serious risk of liability to Disney if the family chooses to sue. Way to early to predict whether they would or not, or what Disney's reaction might be. In general, I'd guess they would settle it quietly.
Going back to my lake place analogy, if I knew about the bears wandering around my property, and I did things which enticed to bears to my property (leaving food on the picnic table outside), and then invited you to sleep outdoors next to the picnic table, and then you were mauled, then you probably could successfully sue me. But, if it's a random thing,and I've never seen bears before, and you were attacked as you moved between your car and my cabin, a lawsuit would be very unlikely to be successful.