I know its not on your list as a stopping point but Riverbanks Zoo in Columbia and the SC State Museum and Planetarium are some awesome spots to visit.
Charleston is one of our favorite places on the planet. We’ve been traveling there yearly for the past 9 years. You’ve gotten some great suggestions. I wanted to add in the Yorktown and Magnolia plantation. Our son loves touring the Yorktown and seeing the planes, etc. Magnolia has beautiful gardens and trails, as well as a swamp boat tour that your kids would like. There also is a small petting zoo there.
Depending on how your kids would do, I’d recommend walking around the historic district. Start at Battery Park. And then go where your heart takes you. There is so much beauty to be seen.
All Charleston beaches are beautiful, but Kiawah Island, which is about 30 minutes outside of the historic district, is our absolute favorite. It’s a private residential island, but there is a pristine and gorgeous county park - Beachwalker - that is open to all. Perfect for families. It is lifeguarded in the summer months. There are changing rooms, restrooms and outdoor showers, along with a small stand that sells sunscreen, toys etc. If you’re lucky, you’ll be able to see the dolphins strand feeding at low tide. It’s about a mile walk to the tip of the island. Depending on how your kids would do, it’s definitely worth a try. The dolphins come up on the sand to eat. Amazing thing to see. There’s also the Freshfields market area that is open air with lots of shops and restaurants. They also have movies outside at night on Fridays. Be sure to stop at the Angel Oak on John’s Island on the way to Kiawah. Google it - must be seen to be believed.
With regard to restaurants, 82 Queen, Magnolia and SNOB are wonderful. All have kid’s menus if needed.
I also quoted what someone else said about Columbia. We’ve spent quite a bit of time there, too, and the Riverbanks Zoo, SC State Museum and EdVenture Kid’s Museum are absolute must dos. Columbia is about an hour and a half from Charleston.
Enjoy!