In professing belief in the Trinity, what Christians are saying—and of course you already know this very well—is that the Father, the Son, and the Holy Spirit are all, and equally, divine: each is to be regarded, therefore, as uncreated, eternal, omnipotent, omniscient, omnipresent, etc. Whatever can be truly said of God can be truly said of each of these three distinct Persons. Nevertheless (odd as this may sound) only the Father is God as such, as can be seen in the opening apposition of the Nicene Creed: “I believe in one God, the Father almighty, creator of Heaven and earth, and of all things visible and invisible.” “The hour cometh,” says Christ, “and now is, when true worshippers shall worship the Father in Spirit [i.e., in the Holy Spirit] and in Truth [i.e., in the Son, who is “the Way, the Truth, and the Life” (John 14:6)]” (John 4:23). The Father is clearly to be given the primacy, but He is worshipped precisely in the Spirit and in the Son, who share His divinity.
This is a point insisted on with special force by the Orthodox East, though in fact, being the clear teaching of the Ecumenical Councils, it is—or should be—the common heritage of all traditional Christians. “Greek theology attributes the origin of the hypostatic ‘substance’ [of divinity] to the hypostasis [i.e, the Person] of the Father, not to the common essence. The Father is the ’cause’ (aitia) and the ‘principle’ (archē) of the divine nature that is in the Son and the Spirit” (J. Meyendorff, Byzantine Theology [Fordham, 1974], 183). St Irenaeus speaks of the Father as having “two hands”, the Son and the Spirit, a metaphor meant to convey both the unity of the common essence but also a certain hierarchy among the Persons who share that essence, and thus to reconcile the two sayings of Christ: “I and my Father are one” (John 10:30), and “the Father is greater than I” (John 14:28).
In the Christian West, of course, the “monarchy” (as it is called) of the Father is somewhat obscured by the addition of the term filioque—”and the Son”—to the Nicene Creed and by the resulting doctrine of the “double procession” of the Holy Spirit. By teaching that the Son is begotten by the Father alone but that together the Father and the Son are the source of the Spirit, the West (at least in the eyes of the East) ends up compromising the unity of the Trinity. I doubt I could prove this, but I suspect that if Meister Eckhart had lived and taught in an Orthodox, rather than a Roman Catholic, environment he would not have felt obliged to distinguish between Gott (“God”) and Gottheit (“Godhead”). The doctrine of God the Father would have sufficiently conveyed the idea of a single, transpersonal, and ineffable Source of divinity.
As long as I’m speaking of Eckhart, let me add that it would be a mistake, in my opinion, for you to try to build a case for the esoteric equivalence of the Christian and Muslim understandings of God primarily on the teaching of someone who is widely—though mistakenly—regarded by Christians as a heretic. (“Christian orthodoxy [does] not permit the attempt to rescue monotheism by attributing Father, Son, and Holy Spirit to some prior principle of origin” [J. Pelikan, The Christian Tradition: A History of the Development of Doctrine, Vol. 2 (Chicago, 1974), 232.) This of course is to take nothing away from Eckhart, whom I dearly love. But if one is trying to persuade the faithful of the two traditions to be more respectful of each other’s theologies, Eckhart is probably not the most useful author to cite! I would instead concentrate on parallels between Allah and God the Father, in relation to Whom, as every Christian is obliged to admit, the Son and the Spirit must be regarded as “subordinate”—though with a subordination, to repeat a key point, which in no way diminishes the full divinity of both the Father’s “two hands”.
I repeat this point to forestall any simplistic “mapping” as it were of the Christian Deity, in which the Father’s supremacy might be misleadingly pictured as a static pre-eminence. Yes, the Father is “greater” than the Son and the Spirit, and this in a sense “solves the problem” (as a Muslim friend recently said to me) of relating or reconciling the Christian and Muslim views of God; of course, Christians will still insist upon “associating” the Second and Third Persons with the First Person, referring to them all as homoousios (“of the same essence”), but this is done in a way which nonetheless protects the Father’s sovereignty and which is thus de jure consistent (at least as I see it) with the prohibition in Islam against shirk (“association”). At the same time one must be careful not to forget that Christian Trinitarianism is not unlike Hindu advaitism. The Vedantist teaches that the Supreme Reality is “not two”, which is not quite the same thing after all as saying that it is merely “one”. Similarly, the Christian teaches that God is “three”, but this doesn’t mean He is not also “one”! What it does mean is that the unity of divinity is “dynamic” in character, as attested by the doctrine of perichoresis (the Greek term) or circumincessio (the Latin equivalent), whereby the Persons are said to share in the common essence or substance of divinity precisely by interpenetrating and “giving way” to each other. Perfect tawhīd for the Christian is thus a matter of henosis (“union” in Greek), not hen (arithmetical “oneness”).