Red Fish is a fabulous restaurant with an equally wonderful wine list.
Almost all restaurants on the Island are very kid-friendly.
As Doc mentioned, in Shelter Cove right across the marina from the resort is San Miguel's (Mexican obviously) which is moderately priced (for a resort community) with consistently good food (and margaritas!). In Palmetto Dunes, where the Beach House is located, is Alexander's which has a little bit of everything and nice atmosphere. Crazy Crab on the north end of the Island is a seafood restaurant that has some other things. The food is good, but the attraction here is the view. The Old Oyster Factory also has a nice variety and a lovely view. The CMs at the resort will give you directions. If you'd like to go back into Sea Pines Plantation at the south end of the Island (it costs $5 but you can come and go all day and there are several things to see back there), there is the Salty Dog at South Beach (mostly for lunch), Truffles at Sea Pines Center, and several restaurants at Harbour Town. Woody's at Palmetto Bay Marina is also good for lunch. We also enjoy Marley's near the entrance to Sea Pines. Have a wonderful trip!