To clarify, Adam, I do believe that crimes should be punished by the state, such as injuring one's children. This is not a way to monitor, regulate, or enforce parenting (as educational checks and balances would be), but a way to punish crime. Stoning idolaters under the OT falls under the same category--punishing crime. It's not a way to enforce good parenting.
Austin, so you recognize Israel's right and required accountability by scripture to punish evil, whether the evil comes from a brother, a son, a daughter, or a wife. Now do you think by analogy that the church has the right to have accountability and place under discipline those within the church regarding the religious education of children?
I would have to say yes. Teaching a child heresy would be cause for church discipline, for instance.