Circulating cyber space is a comment from John Calvin in which he wrote Mary is "the mother of the Lord." Rome's defenders use this statement in various ways to prove Calvin's Mariology overlaps in some sense with their blatant Mariolatry that Mary is the "Mother of God." Rather than reinvent my own wheel, I did a detailed entry back in 2019 entitled, John Calvin, The Mother of God, and the Great Protestant Cover-up.
If you're going to engage Rome's defenders over the phrase, "Mother of God," keep your eye on the ball. I would agree with Dr. White's assessment many years ago when he wrote that "Mother of God" is "the single most misused theological term around." The term points to the deity of Christ, not the nature of Mary. Track down Dr. White's book, Mary, Another Redeemer? and go through chapter five to parse this out. Rome's version of Mary includes her intercessory role as well as deep devotion to her. Some of Rome's defenders will spin you around in circles over Mary's role in giving birth to Jesus Christ but will avoid how the phrase "Mother of God" typically functions in popular piety.