now you've changed the title from mother of God, to mother of God with us.
God is with us in His Son. His Son holds the attributes of God, but, is at the same time, the second member of the Trinity. Hence a different person from God in this perspective and capacity, yet He and the Father are One. Jesus, the Son, was given to us as a sacrifice.....not God the Father.
When Jesus was born He was born with all of His Heavenly attributes, yet He was flesh that walked among us. He has undergone and passed all of the temptations we faced yet we failed.
Christ, as the second member of the Trinity and the Son of God, died for us...not the Father, the first member of the Trinity.
The Holy Spirit, the third member of the Trinity, impregnated Mary. Yet the Holy Spirit is not the "father of Jesus"...or God is with us. God the Father is Christ's Father. And now the Holy Spirit is our Helper and intercedes for us all the time.
Each member of the Trinity is separate yet one. It's a hard concept to understand.
If you keep the Biblical attributes of the Trinity it makes things easier to understand.
I have simply and truthfully presented the Scriptures that show Mary is the mother of God with us.