Glad to see you agree that the title belonging SOLELY to Mary is "the Mother of God With Us". That has a much clearer meaning than calling her Mother of God and it eliminates the need to clarify that she isn't the mother of the Father or the Holy Spirit that the title Mother of God provokes.
I see your point. Poorly instructed/catechized disciples can be blown around by many heretical winds, denying Jesus was born both fully divine and fully human, denying the Trinity, etc..
For one only accepting instruction in doctrine and righteousness from the Authorized Version of the Bible, "Mary is the mother of God with us" is perfectly scriptural. "Mary is the mother of God" is also scriptural since it falls within that same truth and does not, of itself, introduce any error.
People have been wresting the difficult passages of Paul's letters for almost two thousand years, and that applies to the other scriptures as well. It was foretold there would be heresies Since Catholics, who are properly catechized, already understand Mary is not the mother of God the Father, nor God the Holy Spirit, they are not confused.
Catholics can be sensitive to the weaknesses of the myriad of nonCatholic faith communities and sects, with their differing doctrines, without compromising the faith once delivered to the saints. Him that is weak in the faith receive ye, but not to doubtful disputations. For there must be also heresies among you, that they which are approved may be made manifest among you.
Romans, Catholic chapter fourteen, Protestant verse one,
First Corinthians, Catholic chapter eleven, verse nineteen
as authorized, but not authored, by King James