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Actually, we do refer to "Anne" as the grandmother of God sometimes.

Both "mother of" and "grandmother of' most naturally convey ontological oneness, and the frequent and unqualified use of which, and as part of the supererogatory praise given to Mary, constitutes thinking of her above that which is written. (cf. 1Cor. 4:6) For in contrast to the Mary of Scripture, the Mary of Catholicism cannot be honored to excess, and in the Catholic quest to almost deify Mary, then among other thongs, it is taught by Catholics *

as Christ was sinless, so Mary was;
as the Lord remained a virgin, so Mary;
as Christ was called the Son of God, indicating ontological oneness, so Mary is called the Mother of God, which easily infers the same, and is not the language of Scripture, (nor is "Co-Redemptrix");
as the emphasis is upon Christ as the Creator through whom God (the Father) made all things, including Mary, so it is emphasized that uniquely “to her, Jesus owes His Precious Blood,” shed for the salvation of mankind, (the logic behind which can lead back to Eve);
as Catholics (adding error to error) believe Christ gave His actual flesh and blood to be eaten, so it is emphasized that Mary gave Him this, being fashioned out of Mary's pure blood and even being “kneaded with the admixture of her virginal milk,” so that she can say, "Come and eat my bread, drink the wine I have prepared" (Prov. 9:5);
as Scripture declares that Christ suffered for our sins, so Mary is said to have done so also;
as Christ saves us from the condemnation and death resulting from the fault of Adam, so it is taught that man was condemned through the fault of Eve, the root of death, but that we are "saved through the merits of Mary;" who was the source of life for everyone.
as the Lord was bodily ascended into Heaven, so Mary also was;
as Christ is given all power in heaven and in earth, so Mary is “surpassing in power all the angels and saints in Heaven.”
as Christ is the King of the saints and over all kings, (Rv. 15:3; 17:14; 19:16) so Mary is made Queen of Heaven and the greatest saint, and that “Next to God, she deserves the highest praise;”
as the Father made Christ Lord over all things, so Mary is enthroned (all other believers have to wait for their crowns) and exalted by the Lord as Queen over all things;
as Christ is highly exalted above all under the Father, so Mary is declared to be the greatest saint of all, and as having "a certain equality with the Heavenly Father;"
as Christ ever liveth to make intercession for the saints, so is Mary said to do so, to whom "we have recourse, to thee alone," even sometimes as a more immediate and superior recourse for help than Christ Himself, and with her prayers being like commands to God;
as all things come from the Father through the Son, so Mary is made to be the dispenser of all grace;
as Christ is given all power on Heaven and on earth, Mary is said to have (showing some restraint) “almost unlimited power;”
as no man comes to the Father but through the Son, so it is taught that no one can come to the Son except through Mary in Heaven;
and as the Lord called souls to come to Him to be given life and salvation, so (in misappropriation of the words of Scripture) it is said of Mary, “He that shall find me shall find life, and shall have salvation from the Lord;” “that through her are obtained every hope, every grace, and all salvation. For this is His will, that we obtain everything through Mary.”
And as Christ is given many titles of honor, so Mary also is, except that she is honored by Catholics with more titles than they give to the Lord Himself!
It is through God in IHS that Mary receives all the graces we claim she has.
And "to her, Jesus owes His Precious Blood" (http://www.salvemariaregina.info/SalveMariaRegina/SMR-098.html) no matter how they seek to qualify it, "owe" means the Creator is indebted to His creation.