The woman is identified as Zion NOT Mary.
The woman of the Great Sign of Genesis 12 is identified as the mother of the male child who will rule the nations with a rod of iron. This is a direct reference to Psalm 2, a Messianic psalm which describes Him in these terms:
"I will proclaim the decree of the Lord,So that's the Messiah. Mary is mother of the Messiah.
he said to me, “You are my son;
today I have begotten you.
"Ask it of me,
and I will give you the nations as your inheritance,
and, as your possession, the ends of the earth.
"With an iron rod you will shepherd them,
like a potter’s vessel you will shatter them.”
The reference also draws our attention to Zion (Daughter Zion), Daughter Jerusalem, Israel, the Church, Lady Ecclesia, etc. etc.
That's the way Biblical images and types work. They are multivalent. These various meanings are simultaneous; they are not identical, but they rhyme.
With this typical multivalence in mind, we can see that Jesus IS the son of Mary, the son of Daughter Jerusalem, the Son of Zion; as well, the son of Bathsheba and David, the son of Adam and Eve. That is because he is a true member of the human race, and has a true lineage according to the flesh, even though his human nature is joined to His divine nature, and He is the Son of God.
It's beautiful, isn't it?
Yes. You are right.