So basically, we have an alternative scenario.
That CW is telling the truth, his wife killed the kids and he killed her, but because of his social awkwardness, his thinking is so off that he decided to hide the traces of the traumatic night and pretend it did not happen. And during the next day, he dissociates because of the trauma and pretends it did not happen and behaves in such a strange way that the Thayers are concerned.
But here is a major contradiction to this version. His behavior the next morning, the words he said during the intervew, indicate that his thinking is not off. A person "pretending that it did not happen" would merely say "I hope they just are out somewhere". But he says how he loves them, that the house is so empty without their voices, tries to shift the blame on someone potentially "holding" them - in short, he comes across as the person with perfect understanding of what had happened the previous night. To me he looks scared and probably concerned about the police's activity. I would not put much weight into him rocking or crossing his hands on his chest, but in any way, he is totally with it.
At least this is how it looks to me.