Is the trip for 1 adult & 2 kids, or 2 adults and 2 kids? That would determine whether single-level trains (which don't have family bedrooms) are a possiblity.
If you are heading west, I don't think you can top a Kansas City to Minneapolis/St. Paul (KCY to MSP) routing via LA and Portland. Yeah, it's almost four and a half days -- so perhaps a bit too long for the kids to be cooped up on a train -- but you get good to beyond great scenery on all three trains, plus significant time on two of Amtrak's "flagship" trains with upgraded service (Pacific Parlour car on Coast Starlight, upgraded dining on Empire Builder <and Coast Starlight?>). Down sides are short transfers between each train, which limits the time to let the kids burn off some energy and could lead to missed connections/significant "bustitution" en route. If the length is too much, just bail in Portland and fly home from there.
Eastbound, I think Kansas City to Birmingham (KCY to BHM) via Chicago and Washington DC is an interesting route (Southwest Chief to Capitol Limited to Crescent). Total trip time of just over 2 days, with just under 2 days of "train time". Afternoon layovers in Chicago (3 hrs) and Washington DC (5 hrs) give some time to do some sightseeing and let the kids stretch their legs a bit. Arrival into Birmingham is about noon, so a late afternoon/early evening flight back to KCY should be do-able.
Alternatively, you could do the same route with the Cardinal substituted for the Capitol Limited (this would have to be on days the Cardinal runs... I tested with a Saturday departure from KCY, which worked). This route gives you only a two-hour layover in Chicago, and has you change trains after a 6-hour layover in Charlottesville, VA rather than DC. Upside is scenery on the Cardinal, downside is possibly the dining service on the Cardinal and that Charlottesville may not have the sightseeing opportunities that exist in DC (but then again, at that point all you & the kids may want is a park to run around in until they keel over). The other potential concern is delays on the Cardinal, but six hours of layover should be enough even for that ol' Pokey train. Going via the Cardinal also allowed the trip to extend all the way to New Orleans if you'd rather have that as your final destination. It gives you around 8 more hours on the train, but puts you in NO in the evening, so may require an overnight before flying home. Great for the adults, but perhaps not what you desire with 4-year olds in tow.
Again, the eastbound suggestions above would involve travel on single-level trains. The Viewliner sleepers only have roomettes and bedrooms, no family bedrooms. So booking a family of four on such a routing would be problematic. Even three in a bedroom may be difficult to book via AGR, per a recent thread.
Another routing to New Orleans would be via St. Louis and San Antonio (similar to your Houston routing... just going on to New Orleans). This trip would keep you in family bedroom-equipped Superliners, other than the Missouri River Runner portion to St. Louis.
Final suggestion: If you're just looking for a long segment on one train, perhaps Kansas City to El Paso (KCY to ELP) via St. Louis? Almost two full days on the Texas Eagle. Late afternoon arrival in El Paso, so you might have to spend a night there before returning. Not exactly a major tourist destination, but should work if quality family time on the train is the primary purpose of the trip.
And we accept trip reports submitted in Crayon, so your kids are on the hook whenever this trip happens! Good luck with your planning and save up those AGR points!
