Island's Dining Room is great for family dining. They even have an area for kids to dine, complete with kid-sized tables, cartoons on big TV's, and kid friendly food like pizza and chicken tenders.
Emeril's Tchoup Chop should be fine for kids, but this can change depending on the kids. A child throwing a tantrum or misbehaving is going to stand out in a big way here, and extra finnicky kids might not enjoy the fare. Don't worry I'm not trying to scare you, just being realistic. I've seen many kids eat here and I bet your kids will love it. It has a fun, if not a bit fancy, pacific rim feel.
Bula Bar and grill is a fun place near the pool for burgers, wraps, etc, and there is a nice ice cream shop nearby. Great fun stuff for little people.
Other establishments like Jake's American Bar and Orchid Court Sushi are probably not good places for kids, and seem to be geared heavily in decor and fare for adults.
Have fun!