Big picture options:
Madison to I-80: I recall, many years ago, going SW through Dubuque and Cedar Rapids, probably better than heading due south through Rockford.
I-80 to Des Moines: applies to any of the options here.
Options:
(1) I-80 to I-76 to Denver, I-25 South to Albuquerque
(2) I-35 to I-70 to Denver, I-25 South to Albuquerque
(3) I-35 to Oklahoma City, I-40 to Albuquerque
Pro/Con:
(1) I-80 to I-76 is generally pretty gradual gradients, fairly light traffic in my experiences (but those are a bit dated). But, Denver south to Colorado Springs can be ugly, traffic wise. Then Raton pass is about 7800 feet in elevation, and there has been road construction the past few years. I go over that pass multiple times per year, and have done it with a fairly lightly loaded U-Haul trailer, but am quite comfortable with mountain driving and have a truck set up to tow well. You also go over the Pecos, and sections of I-25 north and south of Santa Fe can be a bit exciting.
(2) I-70 might be a bit longer, trending a bit towards the north between Kansas City and Denver. Rather than going to Denver I would cut off onto US24 between Limon and Colorado Springs - you skip much of the Denver to the Springs traffic, but still have Raton etc. from (1) above.
(3) I-35 to OKC has no real altitude gains. From OKC, I-40 to Albuquerque is pretty benign as well. Grades near Tucumcari, Santa Rosa, and through the East Mountains into Albuquerque, but nothing at all like Raton pass.
(3a) If you really want to be adventurous, and see lots of cows, you could go West from Wichita on US400, then on to US54 through Liberal KS, Dalhart TX, and down to Tucumcari. Not many hotel options on that route, so might not be the best for little kids...