You’re right — Jesus battles Satan.
Jesus is the seed of Mary that will crush the head of the seed of the serpent — the devil.
But that isn’t what the official roman catholic bible says.
THE IMMACULATE CONCEPTION
Ineffabilis Deus
Apostolic Constitution issued by Pope Pius IX on December 8, 1854.
...
“Hence, just as Christ, the Mediator between God and man, assumed human nature, blotted the handwriting of the decree that stood against us, and fastened it triumphantly to the cross, so the most holy Virgin, united with him by a most intimate and indissoluble bond, was, with him and through him, eternally at enmity with the evil serpent, and most completely triumphed over him, and thus crushed his head with her immaculate foot.[14] “
14. Quo circa sicut Christus Dei hominumque mediator, humana assumpta natura, delens quod adversus nos erat chirographum decretia, illud cruci triumphator affixit; sic Sanctissima Virgo, Arctissimo et indissolubili vinculo cum eo conjuncta, una cum illo et per illum, sempiternas contra venenosum serpentem inimicitias exercens, ac de ipso plenissime triumphans, illus caput immaculato pede contrivit.
“Our soul overflows with joy and our tongue with exultation. We give, and we shall continue to give, the humblest and deepest thanks to Jesus Christ, our Lord, because through his singular grace he has granted to us, unworthy though we be, to decree and offer this honor and glory and praise to his most holy Mother. All our hope do we repose in the most Blessed Virgin — in the all fair and immaculate one who has crushed the poisonous head of the most cruel serpent and brought salvation to the world: in her who is the glory of the prophets and apostles, the honor of the martyrs, the crown and joy of all the saints; in her who is the safest refuge and the most trustworthy helper of all who are in danger; in her who, with her only-begotten Son, is the most powerful Mediatrix and Conciliatrix in the whole world; in her who is the most excellent glory, ornament, and impregnable stronghold of the holy Church; in her who has destroyed all heresies and snatched the faithful people and nations from all kinds of direst calamities; in her do we hope who has delivered us from so many threatening dangers. We have, therefore, a very certain hope and complete confidence that the most Blessed Virgin will ensure by her most powerful patronage that all difficulties be removed and all errors dissipated, so that our Holy Mother the Catholic Church may flourish daily more and more throughout all the nations and countries, and may reign “from sea to sea and from the river to the ends of the earth,” and may enjoy genuine peace, tranquility and liberty. We are firm in our confidence that she will obtain pardon for the sinner, health for the sick, strength of heart for the weak, consolation for the afflicted, help for those in danger; that she will remove spiritual blindness from all who are in error, so that they may return to the path of truth and justice, and that here may be one flock and one shepherd.” [Emphasis mine.]
http://www.papalencyclicals.net/Pius09/p9ineff.htm
Rom 16:20 And the God of peace crush Satan under your feet speedily. The grace of our Lord Jesus Christ be with you. - DRB
That is correct, but that most certainly makes Jesus neither subservient to Mary nor subordinate to Mary. At the Name of Jesus every knee will bow, in heaven (including Mary's), on earth, and under the earth, and every tongue will confess (including Mary's, as it already has) Lord Jesus Messiah, unto the Glory of Father God.
Being given the unique privilege of holding Him as a babe to nurse and care for never put her in the position of having any authority over Him as a grown person. one Who is not only Man but also Deity all in One Person, which Mary is not, cannot be, and never pretended to be. I would not be surprised to see her horrified at the way ignorant obsequious humans have elevated her despite her real attitude of humility.
But thanks for your agreement in the view of the Genesis 3 passage.