The Tai-Me was a doll about 2 feet high with feathers and mocassins and was used to be present for ceremonial dances and so if it was stolen then it would be considered a great loss and an affront to the Kiowa so it could be involved in their downfall due to their sense of loss.
Because they showed the directer is johns father and then everyone started to make laugh at him.
If the mother goes to the capital to give her speech she would take the kids with her or leave them at home