Do you have one or two drivers? How do the kids do cooped up in the truck for many hours at a time?
600 miles is probably about 12 hours of travel time. I try to avoid driving any more than ten hours in a day because I find my driving ability (and hence safety) drops precipitously not long thereafter due to fatigue, etc. With two drivers to share the work, it's safer, even if the driving isn't split 50/50. Needless to say, different people have different levels of stamina, and driving conditions greatly affect the amount of fatigue, so ten hours is not a universal rule by any stretch. Pushing your own limits is hardly wise in any case.
Many three year olds (and indeed ten year olds) wouldn't be very happy being strapped into a truck for twelve hours in a day. Doing it a couple days in a row is harder.
I would suggest scaling back the trip and maybe only doing things in the black hills area. One day is nowhere near enough time to get more than a quick glimpse of Yellowstone, and it's a fascinating and beautiful area that desreves far more if possible. I'd save that area for another trip.
Bear in mind that this is DrewE's opinion, and worth every cent you paid to get it...but maybe not much more than that.