No, it won't be "cured" by execution, nor will it stop some other depressed parent from doing the same thing. I truly doubt that this woman would ever do this again if she gets the right kind of good help. If however, she ever truly realizes what she did, she could definitely be a suicide risk; as to that, perhaps she should be allowed to do that. I don't know, I am not G-d, nor am I the arbiter of her soul.
It is just too, too tragic, but I also suspect that the US at least, is going to start seeing more and more of this kind of thing for quite a few reasons. Perhaps other "civilized" (whatever the hell that means) countries. Too much Society, not enough caring help. Too much assigned blame, not enough "guilt free help".
Remember the mother in Idaho just a week or so ago? She was "too proud" to accept help, most likely because the "help" offered required her to feel some guilt about her inability to provide. Guilt seems to be a requirement of the current "help" system.
I could be wrong; I was wrong once........I hope I am wrong.