I wouldnt do it. And I am American who regularly did drive cross country, with kids (or rode as a kid). Unless you are attempting to reach home for a funeral, dont do it.
As an adult, my parents lived a 9 hour drive away. We usually did it in 12, taking a long detour to a town with a good park for a long picnic and play break. We also instituted a rule of no less than 4-day trips, which would be two days driving and two days visiting.
When my parents lived in the area I still did, they used to do 2.5 day trips back to where they eventually resettled, so, same trip in same highways. Leaving mid-day friday, arriving at midnight, sleeping until midday saturday, staying up to late, then leaving after church on Sunday to arrive home at around our bedtime. It was horrible and stressful. We saw them less often, but less stresssfully.
Sounds like you need one 'overnight' stop. It could be in the daytime, in a location that would allow at least one driver to nap for several hours, and then drive into the evening with sleeping kids. Or actually overnight and cutting into your visiting time. But really, it's going to be a crap holiday if you spend as much or more time on the road than you do at destination.