I keep going back to one point that really stands out to me and I hope I can explain it clearly...I've been trying to keep up here for hours now and it's quite thought provoking!
"The teacher thought I said I was going to take Kyron with K for a dr's appt...."
This was the day after K went missing...how did TH know what the teacher thought, unless she had planted the idea, as has been discussed here.
To me it's further proof that she did set this up....because I sincerely doubt that LE shared that info with her or anyone.
I would assume that when they (TH and Kaine) realized Kyron was missing and went to the school looking for him, they would have talked to his teacher - who apparently told them she thought TH took him to the doctor's office with the baby.
BTW - there's been debate whether she had the baby with her when she was in the school - to me this would indicate that she probably did, otherwise why the confusion re it being the baby's appointment?