You picked the best SC beachfront state park. You will definitely will enjoy the stay.
Two main trails from the campground to the beach. The one at the north end is much longer than the one at the south end. So if between the two, suggest the south end.
Other advice above about the house tour, the nature center, and geocaching is good advice. The trail from the north end of the campground to the nature center is short, so walk over, don't drive.
Recommend a portable gas grill for the camper. The cheap $29 from Walmart or $39 from Lowe's works well and last a long time. You can either just use the 2lb disposable tanks or buy an adapter for the larger tanks. Much nicer than cooking on charcoal, especially with kids. The gas makes it much more convenient to fire it up for lunch since it heats up and ready for cooking in a minute or two.
To help minimize the sand, suggest a bucket of water by the door and towel just inside. Rinse of the feet before going in and dry on towel. Towel can be changed out or shaken off as needed. Also, make sure you either use the shower rinse on the boardwalk or in the bath-house. With our kids, we preferred the bath house to get the heavy sand out of the nooks and crannies.
Don't let the kids run around the campground barefoot. There are a lot of sand spurs which can be painful. Recommend when going to the beach to wear sandals or shoes until reach the sand at the dunes.
Your pass should also be good for Myrtle Beach State Park just up the road. You can verify at the park office. If so, make sure you go up there and take the kids out on the pier. Don't be afraid to talk to the crabbers and fisherman on the pier. They realize they are in a tourist area and usually don't mind talking. If you get real lucky, may have one of the special locals that enjoy kids, that will make it a special treat. Also check about any kids programs. Often they have crabbing activities or nature events on the beach.
Last advice for the adults, if you haven't tried your local Miyabi, there is one just a couple miles up the road. Japenese style cooking of "americanized" steaks, chicken, or shrimp with rice. Food is cooked on the grill in front of you with a little bit showmanship. Go early when they open for quick seating and early bird special. Or, go to Murrels Inlet for tourized local cousine and pay the high prices.
Have fun and enjoy.
