There’s post partum depression and post partum psychosis, two entirely different animals!
Yes. The law which could exonerate someone is in regard to psychosis -- a total break with reality. She planned this. She sent her husband out on an errand, killed one child, made a phone call and then killed her other two children. She didn't begin her "crazy talk" until after she had spoken to an attorney.
Post-partum depression is not a defense, nor, as someone pointed out earlier, do depressed people make a plan to kill someone and then carry it out.
Two different diagnoses.