1. The mother drowning her children didn't get the rationale from the bible.
2. Abortion clinics aren't exactly non-violent themselves. They kill people. But still: What would be the biblical rational to blow them up.
3. Owning a gun isn't violence against those disagreeing with you neither. But I think one can get a rationale from that in the bible, at least an equivalent one.
Still missing: A rationale for killing those that don't believe in the bible from the bible.
If the woman was raised to believe that there is such a thing as God and that he might speak to her then her delusions were supported by her religious beliefs. I completely agree that she is delusional and that God did not, in fact, speak to her. However, I think that this also applies to Abraham and Fred Phelps and the raging jihadists.
Again though I cannot supply a justification for you and we would have to ask the KKK or the Army of God for their rational. All that I can say is that they do use their religious beliefs to justify their violence. I have no doubt that we would both agree that their justifications are misguided.
I think that the belief in a supernatural entity that dispenses justice in some afterlife for actions committed in this life is where the problem comes from. If, instead, we consider this life to be the total set then it makes good sense to behave in a fashion that benefits us in this life instead of some imagined next realm.
Don't mistake this for a selfish approach. We are social creatures and what is good for the group is good for us. The brilliance of Christ's message is that we are all a part of the same group.