Hi Last Trad,
Great question...one I didn't know the answer to, until I just looked it up, but it's always been in the back of my mind as well.
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Yes, the prayer is referring to Our Lady and not the Holy Trinity. Apparently Her title, "Mother Most Admirable" is not the exact translation. In latin, the title is "Mater ter admirabilis", which means "Mother, thrice blessed". In the 1500s, in Ingolstadt, Germany, there was a priest, Fr Rem, who asked Our Lady what Her favorite title was, and She responded with this one. There's a famous painting in that Church of this title.
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The reasons for being thrice blessed are multiple: 1) She is the Mother of God, the Mother of Christ and Mother of all humanity. 2) She is admirable in faith, hope and charity, 3) She was a virgin before, during and after Our Lord's birth, 4) Child of the Father, Mother of the Son, Spouse of the Holy Ghost.