Personhood is a legal definition.  When a fetus emerges from the birth canal it takes its first breath and becomes conscious.  That's when the baby is legally classified as a "person", complete with all the rights conferred on persons.

I'm reminded of when Henry Hyde, chair of the House Judiciary Committee, held hearings against what he falsely called "partial birth abortion", which is correctly called "dilation and extraction", a procedure used to abort a pregnancy in the third trimester.  A woman testified before him who had had that procedure.  Rep. Hyde called her evil.  The woman had been pregnant with a fetus having no skull, intestines growing outside of its body, and no chance to live.  And, according to her doctor, giving birth to it was a risk to the mother.  Hyde wanted her to go through with the birth anyway.

There are reasons that even third-trimester abortions are necessary, but the Hyde Amendment forces women to risk their lives for his immoral certainty.

When do a woman's rights prevail over those of an unborn fetus?

Always.  It's as simple as that.