Hi Brad! I am originally from Mooresville Indiana too! What a small world! We spent 2 weeks at OBX two years ago. If I were you, with kids, I'd do half the week at Oregon Inlet and half the week on Ocracoke Island. Here's more info ...
Our favorite was Ocracoke Island Campground NPS ... The kids will love the ferry ride (with the trailer in tow). Here are a couple links from my blog on the possibilities. Bike rides into the village, visiting the wild pony pens, hiking, kayaking, ranger talks ... all was great on Okrakoke.
Ocracoke: My "Crabby" Campsite10 Fun Free Things to Do on Ocracoke IslandWe also camped at Oregon Inlet NPS for a week. We toured the lighthouses, the Wright Bros First Flight museum -- the kids would likely LOVE Jockey's Ridge State Park - sandboard or whatever down the huge sand dunes! Link below.
Oregon Inlet Campground. OBXSandboarding at Jockey's Ridge State Park DunesIf you're/they're into fishing, fishing seems to be a popular activity during the day. If I had still been a kid, I'd have had a flashlight out at night chasing the beach crabs - some in our campsite!
Enjoy!