Sheesh, Charles Ingalls has itchy feet, I have itchy fingers...
Ok, with this book, I keep going back and forth about Jack not riding in the wagon. In those days, dogs weren't pampered, farm dogs had a job to do just like every other member of the farm. Charles was being the alpha saying dogs don't ride in wagons, because dogs weren't pampered.
BUT, Jack's role as the watchdog was a very important. The one with the most important members on the expedition to Kansas was Charles, the horses, and Jack. The safety of those three is of paramount importance. Charles, as the human decision maker, needs to take into account fatigue levels of the team and Jack. That's the main mistake he made, not accounting for Jack's fatigue level until after the river crossing when they thought they lost him.