The Quran never mentioned Mary is one of the Trinity’s God, in fact the Quran never mentioned the word God in the Trinity or any name of the Trinity gods in the verse 4:171 as it is “open-ended” to condemn any or all combination of trinity gods.
S4:171 O People of the Book! Commit no excesses in your religion: Nor say of Allah aught but the truth. Christ Jesus the son of Mary was a messenger of Allah, and His Word, which He bestowed on Mary, and a spirit proceeding from Him: so believe in Allah and His messengers. Say not “Trinity”: desist: it will be better for you: for Allah is one Allah: Glory be to Him: (far exalted is He) above having a son. To Him belong all things in the heavens and on earth. And enough is Allah as a Disposer of affairs.
However, Christians who made the God Allah as one of the Trinity is condemned –
S5:73 They do blaspheme who say: Allah is one of three in a Trinity: for there is no god except One Allah. If they desist not from their word (of blasphemy), verily a grievous penalty will befall the blasphemers among them.
The verse that mentioned Mary is not one of the Trinity gods but mentioning her as one of two gods –
S5:116 And behold! Allah will say: “O Jesus the son of Mary! Didst thou say unto men, worship me and my mother as two gods (ilahaini) in derogation of Allah’?” He will say: “Glory to Thee! never could I say what I had no right to say. Had I said such a thing, thou wouldst indeed have known it. Thou knowest what is in my heart, Thou I know not what is in Thine. For Thou knowest in full all that is hidden.
And Allah also condemned those who worshipped two gods instead of Him alone –
S16:51 And Allah has said: Take not two gods (ilahaini), He is only one God; so of Me alone should you be afraid.
Thus, the Quran never mentioned any specific name to form the truine gods in a Trinity.
Pondering with Saifuddin's index 