What does this show about their thought process concerning the events that have taken place over the past year?

Atticus had always put faith in both Scout and Jem to be responsible so I don't think that was a stretch to let them go alone. This, however, shows just how stressful the case was on Atticus and Aunt Alexandra to make them tired enough not to attend the pageant. From a narrative point of view, this allows Bob Ewell to attack the children on the way back.