Matthew 1 20 But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, thou son of David, fear not to take unto thee Mary thy wife: for that which is conceived in her is of the Holy Ghost. 21 And she shall bring forth a son, and thou shalt call his name Jesus: for he shall save his people from their sins. 22 Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, 23 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.
That is not the phrase *mother of God with us*.
She is NEVER referred to by that title.
The only reference to her is *Mary, (the) mother of Jesus*.