[quote=viktor aleksndr]I was really struck on what the Protestants have said that Mary should not be called Mother of God but only Mother of the Son of God or Mother of Jesus or Mother of God the Son.
Any of those titles are appropriate for Mary. The only reason that they are less common in Catholicism is because, historically, they have been used by heretics since the time of Nestorius to imply that Christ is somehow not fully God.
[quote=viktor aleksndr]Does the Church mean when we say that Mary is the Mother of God that she is Mother of God but referring only to Jesus the Second Person of the One God?
Yes, the Church is stating that Mary is the Mother of the Second Person of the Blessed Trinity, God the Son. Because the Second Person of the Blessed Trinity is fully God – not just “one-third God” – it is appropriate to call Mary the Mother of God.