Was Mary the mother of the indivisible nature of God?
Jesus was God incarnate who laid aside His divine perogatives while in the flesh. Now, take all of Scripture into account. Mary gave birth to Jesus' flesh. John writes the Word became flesh John does not write the Word was born flesh.
The Catholic Church teaches Jesus had two natures (human and divine) that are joined by the "hypostatic union". The Catholic Church does not teach Jesus' divine nature was birthed by Mary or the nature of God can be divided.