It's interesting that you say that they have "some independent rights" presumably extending into the future, but you don't accept that they have the immediate right to life
That's...the opposite of what I said.
It's not about primary and secondary rights, it's about a proper understanding of the field of application of each right. Beyond this, no one can be compelled to be a minimally decent human being. That's not what political justice and civil coercion are about.
the rights of the child only exist because the mother has chosen to create those rights by bringing the child to term.
That's clearly not so. Let's imagine the horrible (yet, unfortunately not incredible) example of a woman that is abducted by someone, raped, then kept locked up until she gives birth. Would the child not have rights against her, because she didn't choose to have it in any way shape or form? The logical conclusion of this argument is that if the father doesn't care about it and the mother doesn't want it, they should be free to let it die. Since this is incompattible with any bare-bones conception of justice, this can work as a reductio against any argument premised on the connection between childrens' rights against their parents and their parents' reproductive scheduling.
What's at stake here is whether children have rights against their parents, or what is the same, their parents have duties towards them, or children have formal privileges conferred to them by people voluntarilly taking up obligations towards them. My argument from the beginning has been that the former is the case, that the latter is incompattible with justice due to the unchosen character of coming into life, the principle of equal concern towards moral persons and so on.
You are essentially reframing this as minimising harm to the child
What I'm saying is that existing children, regardless of the circumstances of their birth or of the relationship of others with each other, have rights of care and support against their parents, which can not be overturned. My primary problem with this scheme is that their right to live a certain life would be injured. What matters is not their wellbeing -which, truly, as it follows might be diminished- but the principle under which their wellbeing is administered. Their categorical right to be cared for is what interests me. A circumstance-sensitive (rather than a choice-sensitive) scheme which overturns their rights, is incompattible with their dignity as free and equal reasonable creatures.
another method of ensuring that the child doesn't have an impoverised upbringing is not to bring the child to term.
Sure. But that's orthogonal to my argument. I'm not evaluating whether the mother should reasonably choose to bring the child to term or abort it. I'm evaluating whether one of the parents (I don't care if it's the father) should have a discretionary ability to overturn their existing child's rights. Obviously, non-existing persons are not subjects of the moral law -as they aren't subjects, period- and therefore have no rights which can therefore not be overturned or infringed upon by anyone's choice to do anything.
the rights of one individual that we might consider absolute only exist through the agency of another.
That's not precise. The mother's negative agency (she brings the child to term by an omission, not by an action) is the reason that a subject of moral law is brought to existence. But it's not the reason that all existing subjects have these rights. Her omission is constitutive of a person, not of their rights as persons. Their personhood is constitutive of those.