Mary is the mother of Jesus Christ, who, yes, was called “Immanuel” in an Old Testament prophecy. If you are trying to use that to justify the title “Mother of God”, then I think that is a pretty far stretch.
Good, you confess that Mary is the mother of Immanuel. Do you also confess that Immanuel is scripturually interpreted as "God with us?" Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel. Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.
Isaiah, Catholic chapter seven, Protestant verse fourteen,
Matthew, Catholic chapter one, Protestant verses twenty two to twenty three,
as authorized, but not authored, by King James
They need a LOT less than this to 'justify' a lot of their practices.