I figured common sense would answer that for you but here it goes.
You can't kill your child yet you also have rights over your child greater than any other member of the public.
Are you arguing to argue or do you really not see the false dichotomy in your claims?
You ask where the line exists, it depends on the issue, the jurisdiction, etc. It is not some clean universal line. It is an unenumerated right hence not one clearly drawn but inferred and created through case precedence.
We aren't talking about rights of other "members of the public," but rights which government agencies do not recognize.
So, you're telling us parental rights exist, but there's no clearly defined right anywhere in the law. Doesn't sound like a right -- more like an opinion based on assumptions.
You're no better than the libtards who claim everything they want from government is a right.
Healthcare
food
shelter
a guaranteed income without employment
student loan forgiveness
on-demand abortion without limits
climate change agenda items
and on and on.
Just because you believe a right exists doesn't make it so. Unless the constitution or statutes protect said rights, you have no such legal rights.
As far as parental rights, those are enumerated in law not as rights, but as administrative guidelines. You can make medical choices for your children or decide what religion they will be raised in. Those are not rights as much as legal responsibilities and permitted choices in how to raise them. First amendment covers the latter -- religion.
You can't commit murder ... of anyone. So your straw argument doesn't apply as a some kind of reverse parental right -- something a parent can't do. (We won't go into the millions of children killed by their mothers prior to birth.)
Instead of arguing, try understanding for a change. You enjoying giving your 2 cents in every discussion, yet more often than not, you're just posting to feel involved.