Ok, here is my theory.
Maybe TH was really trying to poison Kaine that morning, and the plan backfired. Maybe she put something in his OJ (anti-freeze?). But instead, Kyron drank it. TH doesn't realize this, and they head off to school.
They take the picture, look at exhibits, and Kyron has to use the bathroom. He comes out and says "mom, I'm sick -- I threw up." TH panics and says "What?! What did you eat/drink before we left?" She immediately realizes what happened. "Come on, we are going to the doctor, hurry!" She tells Kyron to get in the stroller, she covers him up, and they get to the truck. She calls DeDe in a panic, and DeDe tells her to go to the store and get Ipecac syrup or activated charcoal, etc. and try to make him vomit. These may be hard to find. She can't call 911 or they would pump his stomach and discover the anti-freeze. So, maybe Kyron is vomiting, as she is driving around on country roads. She figures maybe he will be okay once its out of his system, but Kyron expires. She freaks, calls DeDe, and meets her on one of the farm roads, where they dispose of his body.
TH goes to the gym, not to workout necessarily, but to shower and dispose of any evidence (ipecac syrup bottles, body fluids/dirt on her hands, etc.). She goes home, emails the school "what time should I pick up the project?" Teacher says "Kyron can just bring it home from school..." Now she knows that Kyron has not been marked absent yet. We know the rest.
I hope to God I am wrong. What do you think?
This is only a theory -- My opinion only -- please feel free to poke holes!