It is not that coercion is always wrong. Self-defence and the defence of others is right. Otherwise evil could win. But when we do intervene to stop one child attacking another, that is a damage limitation exercise, to try to preserve any knowledge creating going on.
Being fallible implies that we can be mistaken including when we feel certain that we are right. And because we are fallible, there is no reliable way to know who is right and who is wrong. Disagreements can either be resolved through reason, or they can be dealt with coercively. So no, feeling that we are right does not justify coercion.
Children are not born knowing right and wrong arises out of the paternalist view of children, which mistakenly holds that children learn moral knowledge through coercion, and that no one would have any interest in improving their moral knowledge unless forced to do so. But actually, coercion impedes and impairs learning, including of moral knowledge, and the vast majority of people including children are trying to do the right thing and trying to improve, including morally, and no one has perfect moral knowledge.
What a moral person would do, and want, depends, among other things, on what he believes the rights of the various people concerned are. And the consistency of this moral background, helps the parties to interact with each other non-coercively.
When I go to other people’s houses, I try to abide by their wishes in respect of their property and so on. I try to make my visit add to their lives rather than detract from them. I try to be sensitive and (to the extent that I think they will want this) helpful in a non-intrusive way. We all want to do the right thing, including our children.
Children have to do what they themselves think is right, with no pressure whatsoever—that’s what non-coercion amounts to—but they also have a right to be told morality as best we see it.