Most of your questions have already been addressed sufficiently.
-Nobody mentioned the Quarter Deck, if unscathed by Matthew, is good dining option too
-Great take-out, & fresh take home seafood @ Risky Business & Harbor House.
-if it rains take the kids for a ride to the toy store in Buxton
-if you have a 4x4 get a beach driving permit
-rent a golf cart if you want to explore Hatteras Village
-visit the marinas after 3:30 or so
Our daughter (now 6) loves Oden's Dock. She starts asking if we can "go to the docks?" early every afternoon rain or shine. She loves the views, the people, the pups, the birds, the fish and the fish cleaning "show" put on by Mr Steve and Mr Chris from Risky Business Seafood. Pack a cooler or grab an adult beverage from The Dock Store and stay for the sunset.
My daughter is almost 15. Trust me, once they get hooked on going to the coast in the summer, there's nothing you can do about it.