With three weeks and dropping Tombstone you can have a great trip. You didn't mention when you were going, hopefully not in July or August when the campgrounds are packed and it is hot. In May is great since still cool enough at night to stop for a short night.
If you make it 4 or 5 hours down the road after work before stopping for the night it would be great, especially if this will get you out the heavy traffic zone. Then I would do one day of heavy driving, say 14-16 hours at max. Make sure to stop every couple hours to stretch your legs and bathroom break. Do not try to drive through the night, that is just asking for trouble, even if sharing the driving. A couple minutes here and there won't add up much but will be much appreciated by your bodies. Then slow down and take it a bit easier. You will enjoy the trip much more if you consider the whole trip the adventure and not just your destination.
Even taking 5 days out and back (500 miles/day), you would still have 13 days to sightsee.