We should. God should be used to refer to all three persons of the Holy Trinity. I think using God to refer to only the Father is dangerous as it can lead one towards a semi-Arian spirituality in which the benefits of Trinitarian thought are lost. We should also pray to all three persons by name. It is important that we read and study the Nicene Creed, which is the CF.com Statement of Faith, and the doctrine of the Trinity, and contemplate God as a union of three persons, the Father unoriginate and the Son and the Spirit uncreated, all three coequal and sharing the same divine essence.
Also, the Chalcedonian and Miaphysite theological principle of Communicatio Idiomatum, which was also heavily used by Lutherans in the Reformation in their dispute with certain Protestant groups which disappeared from the mainstream, and is accepted by most Lutheran, Anglican and other Protestant theologians who study Christology in depth, allows us, because in Christ, who is fully God and fully Man, our human nature is in hypostatic union with the divine nature of the Holy Trinity, without change, comingling, confusion, separation or division, according to Ephesus and Chalcedon, to attribute any properties of one of the two natures to the other. Thus, we can say a man was Transfigured, Resurrected, and Ascended to Heaven, and God was born of the Virgin Mary, and God died on the cross and was buried, or vice versa. This is the amazing truth about the Incarnation of God.
Therefore we should celebrate the Incarnation by calling Mary the Mother of God, and remembering that Christ was both God and Man when we consider His passion and death on the Cross, and His resurrection. The risk that someone could misinterpret us as meaning that Mary was the mother of the Holy Trinity should not concern us, because people will misinterpret anything we say anyway, for the wisdom of God is foolishness to the world.