If you want to include the Grand Canyon, then the route you'd want to take would be I-40, to Amarillo, then down US-287 to Dallas/Fort Worth, then I-45 onto Houston.

Keep in mind, this adds 250 miles, which is about and extra half day of driving especially since it involves some slower, non-interstate travel. The Grand Canyon is also a huge place, and very much worth a minimum of a half day of your time, so I would plan on adding another night to your trip.

If it were me, I'd plan to spend your first night as near to the Canyon as you can afford - it's a pretty full day drive there from LA. Spend the next morning there, but get on the road around noon and aim for Gallup NM. You're then 2 full days from Houston, with Childress TX being about halfway, with several hotel options.


Theoretically, you could make this drive in 3 long days, but I don't think it would give you enough time at the Grand Canyon to make it worthwhile, and it would involve some very long days on the road that will be very uncomfortable for your kids.