How about the coastal route through Kitty Hawk and all the way down Cape Hatteras? The ferry ride from Ocrakoke to Cedar Island is fun if the weather is good. Stay In Atlantic Beach NC across the causeway from Morehead City.

Three and five year olds may not be thrilled by what older kids would be thrilled by, but my granddaughters love Great Wolf Lodge in Williamsburg, VA. It is an indoor water park, and there are plenty of kids their ages. After a day in the car, a night or two would help them unwind, though it probably won't do much for you You can also go to Colonial Williamsburg and let 'em run while you walk around -- all without buying tickets -- after hours. You just can't go in anywhere or park in official lots.

If they were older, I would say a trip emphasizing ferries (Cape May-Lewes), Jamestown, and the ones mentioned by tomfuller would be fun and would lead you off the main highways. But they won't remember it.

I think the kids would LOVE Great Wolf. I think they will not love the ferry ride.
Both of these will make a LONG second day drive, as will anything on the OUter Banks--12 hours to HH.
I would try to make Wilmington NC and just hang out--maybe on the beach. That will still make a maybe 6 hour drive to HH.
If you went on another 1.5 hours from Wilmington, Myrtle beach will have everything. However all along the beach towns will be at least miniature golf, etc.
Oops, I see you say "a day or two". Personally, I prefer getting TO our place and entertaining everyone there. But that is me.

Thank you all. The Great Wolf Lodge looks great. thank you for your suggestions. It is going to be a loooong drive.

Keep in mind that there are huge stretches from southern VA thru NC - if you are on I95 - with seemingly nothing in way of food, fuel, bathrooms. (And the coffee is really terrible).

Gail, that is just wrong. There are plenty of exits with food (google NC barbeque trail), fuel, and coffee. Heck, there's a Starbucks in Rocky Mount, Selma, Wilson and Goldsboro. The exits aren't one after another like they are up north,
For that we are all eternally grateful.

THAT is just silly. AND on south--Fayetteville, Darlington (SC), etc.

I'd go down the Garden State and take the ferry from Cape May to Lewes Deleware. My kid loved a boat ride at that age and it will give them a chance to walk around and get out of those car seats.
Then continue south on the Delmarva, maybe stop at Chincoteague to see the ponies or continue on to Williamsburg for Great Wolf.

Something fun, outdoor and different could be a riverboat trip up the Rappahanock River. It leaves from Tappahannock, goes about 2 hours up a scenic stretch of the river with many bald eagles along the shore, stops at Ingleside Winery for a couple hours, then returns. Tappahanock is about 40 miles NE of Richmond, VA. There's also a big pick-your own berry farm
near there-Westmoreland Berry Farm. They have an amusing stunt involving 'skywalking goats'. It's on a very scenic spot sloping down to the river.

OP here. Thank you all so much for taking the time to provide such wonderful suggestions.

What I was referrng to is the absence of clearly marked rest stops with food and fuel as is the norm on many northeast roadways. I drove this route at least twice/year for 9 years and the problem I had was when I needed a quick on/off stop for fuel or coffee. Certainly there are merchants along this route - people live there - but finding them was more challenging than I expected since it was not possible to tell from roadway signage if the service was 1/10 mile from the highway or 10 miles.

Yes, gail, we got so that if we couldn't see the food/fuel place from the hwy we wouldn't get off.

All the ramps off of interstates here have the service and the distance marked as you get off. There are some up on I81, when you get off, say Exxon 2.3 miles. When that happens I just get back on the road for the next one.
Looking at the various crossroads off I95 in NC, I see pretty major places, and even "Smithfield Center", which sounds like a boony place, is a huge outlet mall.