The term *mother of JESUS* is the term than actually suffices to address that Title.
It is specific enough, where as the term *mother of God* is too ambiguous to automatically imply that Jesus is the One who Mary is the mother of.
It is not the only title. The reason Mother of God is effective and useful is firstly because it is true, and secondly because people who deny it do so on basis that obscure the salvation of mankind.
Mary is the Mother of the "Kyrios," the Lord God and Savior. (Lk 1:43)