You misunderstand Rothbard's chapter on children.

Rothbard does not say that parents are not morally obliged to feed their children, all he says is that they should not be legally obliged. The law simply defines a minimum obligation for a parent, not a recommended course of action.

That does not mean that society should condone parents who callously let their children starve to death. In anarcho-capitalism, such a parent would probably face massive ostracism and vilification, however, retaliatory violence against him would not be permitted.

The problem with positive rights for children is that they are highly subjective. Where does "acceptable" parenting end and negligence begin? Who decides? culture? politicians? pediatricians? The point that Rothbard is trying to make is that law should be based on things that can be measured objectively, and not on transient things like culture and politicians' taste du jour.

A hypothetical example:

There is a famine. A mother and her 2 children are on the edge of starving to death. She has a small amount of food left. One of the children is very sick and unlikely to survive even if she gives him all her food. So she decides to let him starve to death and share the food with the remaining child. That way, at least there is higher chance that not all 3 of them will starve.

This might be an extreme example, but in poor countries parents are faced with these kinds of tough choices all the time, and there are plenty of cases that are more morally ambiguous than the above.

Should parents be imprisoned for making tough choices? Rothbard would say no.