I am speaking here not as lotsocats, but as Dr. Duncan, the chair of a university Psychology department, college professor, and clinical psychologist.
With psychosis, the brain has become seriously injured for whatever reason (I could go into the reasons and the type of damage to the brain if anyone wants this information). Because of the problems with the brain, the person can no longer think and process information the way "normal" people do. So, the psychotic person might honestly believe with all of their heart and mind that their children are the devil or that the children should die in order to be saved or some such bizarre thing. You could show them all of the evidence in the world that their belief is not true, but because of the problem with their brain, they cannot change their mind.
Thus, if she truly has Post-Partum Psychosis, because of the changes in her brain that were likely caused in part by the pregnancies, she is (or was at the time) physically incapable of knowing that the murders were not the best thing to do for her kids.
Think of it this way....to ask a psychotic person to think in a rational way and to behave in a rational way is the same as asking a person with no legs to run a marathon. -- Most psychotic people respond fairly well to medications which help straighten out their thinking, just like most amputees can use prostheses to walk. BUT, there are some psychotic individuals who do not get better with medication (just like some amputees can't use the false legs). Apparently, she was one of those folks who does not get better with medications.
So.....do I think she was guilty of murdering her children? You bet! Do I think she was "insane" at the time? You bet! Do I think she should be put to death? Absolutely not! Instead, I think she needs to be under intensive psychiatric care until they can find a treatment that will clear her thinking. After that.....hmmmmm, I'm not sure what I would do; but I certainly would not kill her because she was physically incapable of thinking rationally at the time she killed the kids!
Okay...I'll step out from behind the podium. As lotsocats (rather than as Dr.D), I think someone needs to punish her husband....clearly he could see how sick she was, yet he kept getting her pregnant! What an idiot! While I know that it takes two to tango, he had to have seen that she got worse with every pregnancy, especially since the MD told them not to get pregnant again. So, I hold him partically responsible, not only for helping her get pregnant (which made her even more sick), but for leaving the kids with her 24 hours a day despite knowing what a huge psychological mess she was!