I would take I-49 to I-20 west to US 69 near Tyler. Then north to US 82 north of Bells and then west to US 287 at Henrietta. That is good highway and bypasses the DFW area and the traffic and construction.
Then US 287 to I-40 west to loop 335 around the northeast side of Amarillo. Then US 87 to Dumas/Dalhart/Raton. Then I-25 north to Colorado Springs.
As for miles and hours, it all depends on you and your family. With stops for food, fuel, and rest you can count on averaging around 55 mph on most highways. Maybe a little better on interstates or equal. A "quick" stop can kill your average. So think about how many hours you think the family can stand each day.