As others have noted:
Day 5 (Aug 10): leave Custer around 8 am & head to Cody making a pit stop at Devils Tower. Stop and camp for the night in Cody.
Devils Tower will chew up 3-4 hours, as it is a bit off the Interstate. It's neat, but can be skipped.
I assume you're going from DT through the Big Horns to Cody - extremely scenic drive BUT very slow, twisty turny, long sections of mountain driving. Another reason to skip DT.
Prior to that, see if you can jigger the trip to spend a night in the SDak Badlands, near Wall. The KOA there is recommended - or the campgrounds in the park itself. First real "scenic" area you will hit on the drive, and worth an overnight, and a slow drive through in the morning (takes a couple of hours). More bang for your vacation time buck then Devils Tower. And then you have a shorter drive to the Black Hills, which will allow for better spirits when dealing with the traffic there.
