It's not a ancap position to take to compel others to do anything, whenever there is a doubt. And, honestly, there should be doubt on your part concerning other peoples' children.
Oh, but it
is an AnCap position to compel others
not to do something, for instance to not hit someone. That's called "defense," and it most certainly can be used third-party, especially when the person being defended is incapable of defending themselves against the aggressor. There is no doubt. A person hitting a kid is attacking a defenseless person.
If you can justify intervening with force on behalf of my child, based solely upon your own judgement as to what constitutes initiation of force, then you can justify any singular or collective action at all; and morality truly becomes relative.
No, it's not my "judgment" as to what constitutes initiation of force. I'm simply applying the same standard to adult/child interactions as I do to adult/adult interactions.
It's your own
perception of a particular situation that requires judgment, and that is the problem.
Where, exactly, in your moral code, do these two phrases differ, that one would be justifiably responded to with deadly force, while the other would not?
"Hey, stop raping that woman!"
"Hey, stop hitting that kid!"
Hey Myrkel, when did you stop hitting your wife?
Both of those statements are context dependent, and your are trying to
imply that a particular situation, and your own perspective on that situtation, is correct. It also happens to be a strawman argument, but that's not really important.