@Spoletta:
I think we both have a completely different take on what is acceptable, and not acceptable in a civilized society.
To start, it is incorrect to assume Libertarians are just a singular unified ideological block. However, when it comes to rights, defining what they are and where they come from, Libertarians are fairly unified. Rights are, by nature, "negative". This basically means a "right" is something that requires us to NOT do something. For example, you wouldn't say that you have a "right to life". Rather you would say that you have a "right not to be killed." If you did assert that you have a "right to life", then that might imply that others have an obligation to give you a fresh liver after you have ruined yours by excessive drinking. Likewise, you don't have a "right to property", you have a "right to not have your property stolen". If you have a "right to property", then you might infer that you have a claim to a yacht.
This view is also important because it defines rights outside of something a person, organization, or government gives to you. Also, it builds a pretty solid foundation against slavery, and it is not a controversial one. This is traditionally how rights were viewed, private property rights being pivotal.
This is also the position, I believe, that Simon spelled out several times. But actually, it's still not completely precise. There is one more distinction to be made, and I think this distinction helps a great deal with the issues you have raised below. Let me give you an example: A woman invites you onto her airplane. You go (because of free drinks, of course). Fifteen minutes into the flight she asks you to get off the plane. She asserts it is her property and you are now trespassing. Should she be able to make you jump? The answer is "no". The reason is the plane owner bears some responsibility for you being in your current position. Your actions can obligate you into doing something. You have private property rights, but not to be point that exercising your rights absolves you from your responsibility regarding the consequences of your actions. You might say that we are against involuntary positive rights (involuntary obligations).
Moving on...
Am I not correct that the Libertarian view of children, is that a mother or father may not inflict physical violence on their children, ...
Yes. That is correct.
but should be allowed to let them die of neglect, by withholding food, shelter, or clothing, because to require this would infringe on their liberty, or freedom to do as they please with their property?
Some Libertarians hold this view. However, in the Rothbard article, he says parents have moral obligations to take care of their kids. However, he argues against legal obligations. But what do you expect, he is an anarchist. Interestingly enough, even anarchists, break with Rothbard. And this should show that you can't just point to one Libertarian, find a position, and go on a smear campaign. Consider this article, written by none other than your favorite anarcho-capitalist, Walter Block, on lewrockwell.com. Actually, this might have been the article you first found. I think this might be the case because the lewrockwell.com overall article title is "Children's Rights?", which is closer to your first article title: https://www.lewrockwell.com/2013/06/walter-e-block/childrens-rights/
Notice the quote from Block:
In order to ferret out the libertarian perspective, we must get back to basics. Children occupy an intermediate ground between that of animals and other adult human beings. (I know, I know, this sounds a bit weird, but hear me out.) The former can be owned and disposed of at will. The latter, apart from voluntary slavery, cannot be the private property of anyone else. Children, in sharp contrast to both, may be controlled by parents, under a very different type of legal provision, not ownership, of course, but, rather, attainment and retention of guardianship rights. This means that as long as the parent is properly guarding, safe-guarding, caring for, bringing up, the child, he maintains his right to continue to do so. (bold mine)
I highlight the last part for a reason - the guardianship rights come with obligations. You accept the rights, you accept the obligations. These "guardianship" rights are a bit different than owning a piece of land, a horse, or a spatula. Parents, whether they like it or not, are obligated by their actions, to take care of the child. They can give up those rights and obligations. But they can't be taken. Parents are responsible for the child being in the situation he/she is in (whether that's from an explicit adoption or a pregnancy), much like the plane owner in the example above.
Does this philosophy also mean that they have the right to sell their children?
They have the right to sell their guardianship rights, Yes. But notice - this is what happens now. First, you are allowed to give away your children. Also, you are allowed to become a surrogate for money, or even arrange an adoption, accepting medical care and other cash payments for this service. The original Rothbard article bears this out. Even Rothbard says in the article that, at first, this seems like an odd position to take. But he takes the same "on NET" position. You might think it would be worse, but when you consider all of the effects it would have, he asserts you would find a better scenario for a lot of children and parents. This does NOT in any way advocate for child slavery, or human trafficking. You have to read the position carefully, and always remember what you said above - "Am I not correct that the Libertarian view of children, is that a mother or father may not inflict physical violence on their children". If you, on principle, argue against this, I would expect you to make the same arguments against any sort of money being exchanged during adoption. The average base cost for a U.S. adoption agency is around $40,000.
That's what I take from this article. If I'm wrong, please tell me what I'm misunderstanding. I'm sincere. I don't see any other interpretation of what I just read. I'm not trying to smear anyone, I would really appreciate your take on this.
I hope this helps. But notice - please notice - this has NOTHING ... AT ... ALL... do with the economic arguments made by Mises. And Salerno was just presenting those arguments and the actual historical examples of how they played out. We are here, now, talking about children's rights as a "gateway", like an idealogical test on a side topic, in order to finally be allowed the privilege to engage on the original topic. It is not good.