OK, there's a few things to discuss.
God is love, yes, because love is God's being. Infinite-light-love-being. Glory. And, of course, God's love was expressed, because, to begin with, God's love, His being, is The Power which was necessary for creation to be wrought. The Spirit of God, the Ruach, is the formless Power which existed primordially along with the polarities of the Panim, which is the Presences of the Father and the Son. The Ruach and the Panim: the Trinity. The Panim have identical form by virtue of polarity, but polarity never faces the same direction. The Son is the express(ed) image of the Father, who's countenance we cannot see, or we die.
The Trinity is true because there has to be a prime mover and polarity, for creation to exist. Though in three parts, there can be only one God, in essence. If there were three Gods, then there would have to be a fourth God who existed before them who created them. That is what would happen if The Spirit of God was different than The Holy Spirit; but The Power is the same as The Paraclete, though differing experientially in position and intensity.
Incidentally, in a contest between an irresistible force and an immovable object, the irresistible force would win;
by attrition.
The Trinity can be thought of in mathematical terms, which is something that Rene Descart speculated upon. My thought in this regard is that in eternity, the Trinity is 1=3^0, and in temporality, the Trinity is 1^3=1. So, like an hourglass between heaven and earth, 3^0=1=1^3. However, this is just a simple mental illustration.
The nature of the Trinity during the incarnation of Jesus is not so easy to understand. I see it in terms of a pinhole camera. A camera doesn't need a lens, if the aperture is very small. In order for the Word, the Logos, to become incarnate, one polarity had to squeeze through a pinhole, into a very small cavity that is a vessel. In order for the vessel to not break, most of the Glory had to be left behind, with the Father. While the sentience of the Son existed in the vessel, a pinhole connection to His distant Glory and the Father/Power meant that certain capabilities were restricted, and so it was necessary to follow instructions; and so there was some information which was not given, for good reasons. You can call His earthly condition a state of temporarily distended omniscience.
When Jesus called out, "My God, My God, why have you forsaken me?", He was calling out to both the Father and the Power. That shows that the Trinity was intact throughout His incarnation. Further, forsaken does not mean deserted. It means that Jesus was experiencing the occulted Trinity. The Father/Power was hidden from Him because of the burden of sin which He took upon Himself. It is as if thick dust was shaken loose by an earthquake into the focal frame inside a pinhole camera. As Jesus previously referred to this, "the night is coming when no one can work" John9:4,5 which was from then until the resurrection. The resurrection is when Jesus overcame sin. As He did not die spiritually, but only physically, and He was the Word made flesh, His flesh could not stay dead once sin had been cleared away by atonement, which was like a spark in a dusty grain silo. Once the "dust" of all believers sins had been consumed by holy fire, then the occulted Trinity reverted back to at-one-ment.
I'll save the discussion of the seven Spirits of God for later, God willing.
Of course, this is all still only an approximation of Truth, but it's pretty good, for a human tongue, in English speech.