Rothbard’s plumbline position in “Kid Lib” (1974) and The Ethics of Liberty ch. 14 (1982) is that parents have a right to set household conduct rules, as the proprietor of the household, until children move out and take up living on their own; but that parents have no right to physically aggress against children [*], that children should be able to legally prosecute parents for injuries committed against them in the name of “discipline,” that children have an unconditional right to end their parents’ guardianship at any age where they are physically capable of running away, to strike out on their own or to take up with any foster parents who agree to take them in, and that neither parents nor the State have any right to force “runaway” children to return to the guardianship of any adult against the child’s will.
In “Kid Lib,” Rothbard aims to position his view as a middle-road between traditional coercive parenting and (his notion of) “Progressive” anything-goes parenting, with most of the rhetorical energy being spent on the latter, so he spends a fair amount of time grumping about kids “kicking adults in the shins” and discussing how he thinks that parents should insist on rules of conduct and a certain degree of unilateral authority, but that it must be on a “my house, my rules” basis and not on the basis of using physical or legal coercion to keep the child captive. But the last, which he views as “the fundamental tyranny” of the contemporary parent-child relationship, he denounces as “kidnapping,” and as “enslavement” of children by parents.
In “Ethics of Liberty” most of the stuff about theories of parenting and house-rules is dropped in favor of a more systematic examination of children’s rights, with a long section on the violation of children’s rights by statist law in particular, with highlights on the evils of truancy and other Fugitive Child laws, use of catch-all “juvenile delinquency,” inquisitorial proceedings without basic due process rights, the parens patriae doctrine, etc. to extend and intensify the power of abusive parents over “wayward” children, or to step in if a parent isn’t vigorously abusive enough, etc.
[*] Rothbard talks about “mutilating” and “abusing” children as aggressions and as violations of the parent’s role as trustee for the child’s self-ownership. I think his position logically implies that it’s illegitimate for parents to use any form of corporal punishment at all against children, but as far as I know Rothbard neither confirmed nor denied that in his writing on the topic.
As far as I know, even after his paleo turn, Rothbard never actually declared that his prior position on children’s rights was false. (He actually hardly ever repudiated any ideological positions, no matter how many strategic 180s he did; just swapped out his rhetoric and tended to write a if he had never said the things that he said before.) But by 1992, mainly in the interest of demonizing Hillary Rodham Clinton, he was scare-quote ridiculing any discussion of children’s rights, declaring that children should quote-unquote “get governed by their parents,” and denouncing Tibor Machan for supporting children who sued their parents for damages or for termination of custody. (I haven’t read any of Tibor’s stuff from that period, so I can’t be sure, but from the date and from what Rothbard writes, my guess would be that this was in response to high-profile cases like Kingsley v. Kingsley, in which a child was granted legal standing to sue for a transfer of custody from his biological parents to foster parents. Anyone know for sure?)
Anyway, after the paleo turn, Rothbard was looking to hook up with political allies who took rock-ribbed conservative positions on parental control, so all that stuff about the rights of wayward children and the use of state violence to keep children enslaved to their parents was pretty quickly dropped out, in favor of a line about the state’s meddling in parental rights, with folks like Hoppe throwing in paeans to the authority of the paterfamilias and the order of rank within the family, and the occasional supportive shout-out to the pro-child-beating conservatives from LRC.
Of course, after Rothbard’s paleo turn, there were still plenty of other non-paleo anarcho-capitalists who differed with Rothbard and with his newfound allies on all this stuff, and who generally took something more like the older Rothbard line. (George H. Smith, for example, defends the early Spencer’s position against parental coercion.) And the decline of paleolibertarianism (both as a strategic alliance and as an ideology) since Mr. Bush’s wars and the rise of Red State America has resulted in a pretty significant drop-off.
Most anarcho-capitalists, however, just don’t write about the issue at all. Presumably because they either don’t think about it, or don’t care, or both. Which is unfortunate but not surprising: most political theorists don’t spend much time discussing the status of children. Not because it’s unimportant to them (patriarchal authority is very important to lots of theories) but rather because they have reasons for wanting certain bedrock commitments to be left unspoken so that they cannot be identified, and without any explicit defense so that they cannot be challenged.