This sort of thing happens when a person has simply lost all hope and all sense that they can cope with a situation...and they can't figure out what to do about it...and they break under the stress and lose control. It's an act of desperation. Who knows why? You would have to be her and live her life (all of it) in order to even begin to know why.
Of course some Texans are calling for the death penalty. Duh. It's their standard way of resolving human tragedies after the fact. That's what you get when you combine a serious lack of empathy or imagination with a fearful and vengeful mindset, and just plain outright ignorance.
As if executing her will help anyone....!
It's clear from the story that the woman was in a lengthy and deep depression, that she had lost confidence in herself and her ability to raise her children properly. When people are very depressed it alters their whole perception of reality. Their self-worth goes down the drain, and their ability to cope with ordinary things is severely curtailed. That can lead to suicide or it can lead to other desperate acts which a person would normally not consider. (Animals will also sometimes kill their young when under unusual stress...it's not an act indicative of evil, but of panic or loss of control on some level.)
My only reaction (aside from disgust at those calling for her exection) is sadness.
If she is sent to jail, of course, she will get routinely viciously beaten by inmates who see their own darkest fears mirrored in what she did, and take it out on her. It would probably be wiser to place her in a safe place in some mental institution.
There is no good or easy solution to this kind of tragedy once it has happened. No simple fix. Not even in Texas. No matter how many more lives are taken by the State. Those who are against killing ought not to do it themselves.