How long is your trip? Heading for Texas the first stop would be one of the several Schlitterbahn parks. http://www.schlitterbahn.com/
There are several things in the New Orleans area that would appeal to kids. For Arkansas, the things that come to mind are
The Clinton Library and the state park where you can look for diamonds. Pack the sunscreen if this is a summer trip.

Also in Little Rock, just down the street from the Clinton Library is the Museum of Discovery. It was recently renovated and gets great reviews. http://museumofdiscovery.org/

What month?
Buffalo National River is my favorite in Arkansas. I like Upper Buffalo the best. I could list several hikes that lead to some serious nice waterfalls(depending on which month).
I also like Petit Jean, Mount Nebo, and Mount Magazine State Parks.
Clinton Library as mentioned
Crystal Bridges Museum in NW Arkansas is fantastic.

Hot Springs Horse races is good, especially Derby Day. I don't really care for Hot Springs National Park that much, but it is ok for a few hours.

I like Plantation Homes on River Road and of course, NO in LA

Texas is a big state, which part?
I like Schlitterbahn already mentioned
Guadalupe National Park and Carlsbad Caverns
Big Bend National Park
Shopping and dining in Dallas
Several options along the gulf

Lived in OK all of my life. Not really that many things I would go out of my way for here. I think the OKC Memorial is a nice thing to see.

Six Flags, Alamo, Sea World, Riverwalk are all nice in San Antonio.

Depending on which month you go, a professional sporting event.

Kids, old and young will love Schlitterbahn. Big Bend, altho out of the way, is awesome. Alpine has a very good museum of the Big Bend and is an interesting little oasis in the middle of the desert. Nearby is Fort Davis and the restored, reinacting fort of the "buffalo soldiers". TX is a huge state, varied and interesting. Macdonald Observatory is also worth a stop, near Alpine/Ft. Davis. The unexplained Marfa Lights are always mentioned as a draw in the area but I've never seen them and have looked on many trips.

Good gosh, how can you get good answers without a good question?

(1) Where in Soonerville are you? If you're in the northeast corner of the state, much of Arkansas is thisclose to you so you ought to know where to go. If you're near the I-35 casinos and the Red River, that's no longer true. Seriously how can we tell you "where to stop & what to do along the way" if we don't know "the way"?

(2) Where do you want to go and what do you want to see? Or are you trying to get the board to plan your trip for you? Arkansas should have many state and national parks that could be interesting, Louisiana has swamps and tours thereof so you can see various swamp critters (nutria, waterfowl, gators, Cajuns). It also has plantation homes that would interest an 8-y.o. girl more than an 8-y.o. boy (and you have a _____?). New Orleans' Aquarium is world class, but are you going to the Crescent City?

(3) Texas is not small. Are there particular areas you intend to visit, pass through and/or avoid?

Big R is correct - how much time do you have ? What is your intended route, etc. ?