they ignore any problems with the sister, or signs she might not be the miko, and get rid of anyone who has issues with her, like the teacher who is supposed to train her in manners, until something that is impossible for those around the miko occurs, and then they only act in secret until it is to late.
The problem is they had a divine revelation of the age and location of the miko, but did not double check to make certain there was only one child when the parents only displayed the sister, so as far as they know she IS the miko, because there was no other candidate. The lesson here is keep an accurate census of births and population levels.