* possible, the right to know and be cared for by his or her parents*
They mean the biological parent of the child. The Jurisdictions that have changed have done so because a child has a right to know and bond with it's biological family, unless it would be harmful to them.
And yes, re the stress to the unborn child. If I was the OP, I would explain that I plan to have a paternity test after birth. If I require an amnio for other reasons, maybe we can do it then. I would explain to boyfriend that he isn't my boyfriend and partly because of that and the tiny chance he is the dad, he won't be attending any prenatal appointments or the birth. I would reiterate that if there was a higher chance and/or we were on better terms, I would encourage him to have a more active role, but it isn't like that. I would promise to keep him updated on any significant health complications in regards to myself and the baby, and I would tell him when I give birth so we can prepare for the test. That's it, cut ties until we know who the Daddy is for sure.