If you were getting in the van and making the kids sit for 45 hours then I would agree with your husband but I don't understand the use of his words otherwise. If you leave Texas and make regular stops then it makes the trip much more tollerable for the little ones. With a 2 and 3 yr. old I would say you must stop every 2-3 hours and have play time, whether it's McDonalds or an elementary school alongside the road. Plus I would add some sight seeing stuff into the trip. The older child will have different interests and it may be hard to blend activities. I prefer to get in the car after dinner and travel with a stop for snacks and play time around normal bedtime then get back in and hopefully the kids will drop off and you can continue your trip for another few hours, Then stop and get some rest in a hotel. You'll be less cranky and feel better overall.
If you visit Omaha/Lincoln area I recommend the SAC museum. The space craft and planes are very interesting to guys and the other kids will like it too, but it is a no hands touching kind of place, look only. My favorite place in that area was Freedom Park. You can climb all over submarines (USS Marlin), boats (USS Hazard), WWII helicopters and ambulances, etc....lots of running around and climbing...there's even a boat (an LSM-45) in the river at one end. My favorite picture is of my husband sitting in the seat and pretending to shoot the guns....I have nearly one whole scrapbook of the 2 museums.
We stopped and did the museum in Hastings (Koolaid was invented in Hastings) and enjoyed the IMAX theatre. We also went to see the trains at Cody Park in North Platte. The kids can climb all over the Union Pacific Challenger, the worlds largest steam locomotive. There is also a area that has an animal reserve in it in the same park. It's worth the drive and visit.
If you have a well planned trip then it will be interesting for everyone and they will always remember the wonderful event. There are many different things to see and do, that appeal to everyone. Some things are free and you can choose which pay sites you want to go to. When we went to South Dakota we didn't go to the museum for Mount Rushmore, we had seen all the specials on the History channel so we felt it wouldn't give us any more of an experience than to see it from the parking lot, that was about $50.00 we saved.
When we were on our honeymoon we went to Provo to visit my cousin and go to Conference and stopped at many different places too. My favorite was Dinosaur National Monument in Vernal, it is awesome, I had such a great mental experience there, it felt like dinosaurs we real after that. In OKC there is the National Cowboy Hall of Fame, lots of places like that all along the way.
I know that will take time away from your family but it may make the vacation a bit more of a memory for them instead of must memories for the families you'll be visiting. You can get online and order free visitors guides for just about every state.