You failed to mention that the man should have had custody of the kids. Obviously, if the woman is too broke to feed the kids, the kids need to go with Dad. The fact that the woman doesn't have the wherewithal to care for the children is proof enough she is an unfit mother.
You want to give the woman all the power, but yet you hold her completely unaccountable. Isn't that kind of Nero-like? The maximum incentive for making stupid decisions goes to the woman.
Why was the woman so quick to spread her legs for a man she considers a bad father? Why was the woman so stupid in her choice of men? Why does a woman want to have children she cannot care for? Why is the woman so selfish in forcing the children to live with her broke ass instead of them going to where the money is - with the father? It sounds to me like the woman you are describing should have had her ovaries removed and let the childbearing go to a better woman. If this is your ideal of a good woman, I certainly do not pledge allegiance.
But because you do support such whorish and stupid becoming mothers, I'm doing my part in helping men not fall victim to them through the Great Whore.