My family (Myself, wife, 6yo daughter & 4yo son) can manage 2 days of back-to-back 600 miles, but then we really need to rest. At first the kids would lose cohesion at about 400 miles, but after a few trips we found a pattern that worked for us and now the 600 mile days don't lead to any unhapiness.
Our method is to hit the road very early and get a couple hundred miles in before the kids become very active. Then we start stopping every 60 to 80 miles for leg stretches, snacks, view points, etc. Our average pace slows alot in the afternoon between lunch, dinner, etc. Then once it's dark we just drive for another couple hundred miles until roughly 11:00ish. The kids usually sleep once the sun goes down, and I'm a night owl so i don't mind driving at night. On these travel days we usually don't stop at campground, just because I don't like driving in that late and disturbing others. We stay at rest areas, Wal-Marts, etc. We've done this many times for 2 days in a row, but I don't think I'd try for more until they're older. I hope to be able to get 3 or 4 days in a row out of them by the time they're as old as your kids.