I think the issue is it's not a few "longer stretches" of driving - it's every other day of driving for 8 weeks. You have only one or two 2-night stays during the entire trip.
I get that you aren't a hang out at the campsite type of family and want to see as much as possible. However, your schedule is SO tight that you have absolutely no room for adjustments - whether due to mechanical failure, sickness, unexpected desire to see something else, or just a bad day. There also isn't any time set aside for meals, fuel stops, etc. And while you're a young family on the go - I suggest you look at your daily routine, I suspect you'll find there is a level of downtime that is required to keep everyone from getting cranky.