We of the Libertarian Party are still assembling our famed "Shun List" which you can carry around with you always once it gets published. Keep an eye out at our website: www.lp.org/shunlist.html.
Umm, it was a anti-abortion advocacy piece.
It is impossible to ensure that parents do anything remotely of the sort -- I don't care what form of society you live in. How do you ensure a crack-whore on the streets of Detroit meets parental obligations?
Parents do not own their children. Children have the same rights against harmful aggression as adults, and therefore ANYONE may rightly come to their aid. Societal structures exist to help ensure that those coming to the aid are not at cross-purposes to each other -- and that they aren't acting in a predatory manner.
Therefore parents who are harming or sufficiently neglecting their children simply forego the access to the stewardship of their children -- it would be little different than today.