You are exactly right. Perhaps more than you even realize.
The doctrine of the Trinity explains how God can be One and God can be Love in God’s very nature. If not for the Trinitarian relationship of persons within the One God, then God could not be eternal love. God-as-love would only begin with the creation of an object of that love. But a three-personal God means that God is love, even prior to any created object of that love beyond Godself.
And we must insist that Trinitarian Christianity remains monotheism. We don’t worship three Gods. Orthodoxy proclaims the One God: Father, Son and Holy Spirit, one in essence and undivided. Note: forever undivided. This is a significant problem for any atonement theory that imagines Father turning from Son. Love ceases? Never. Union of the Godhead is interrupted? Not for a nano-second!
You mention the “Euthyphro dilemma” … named after Socrates’ dialogue with Euthyphro in Plato’s work, Euthyphro. I’m glad you caught that. Spot on. In Socrates’ words, “Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?” In modern lingo, the essence of the dilemma is “Does God will only to do good because he is the Good? Or is the good called good because God wills it?”
This is not one of the ‘how many angels can stand on the head of a pin?’ abstractions. It has enormous ethical significance and here is why: If God is good / love in God’s very nature, then to obey God is ever only to participate in the good. I.e. loving God, loving my brother/sister, loving my neighbor, loving my enemy. If God is love by nature, then participating in the divine nature is heeding the call to love.
But if the good is defined as ‘whatever God wills,’ then if God wills to kill and destroy, then that makes killing and destroying good. And if God commands someone to kill and destroy, they are doing good. But what happens? We will to kill and destroy and then justify it by projecting that desire onto God and by claiming to be the obedient agents of God’s will.
We see both these theologies of God across the scope of the world religions, represented in their various scriptures and even competing within the Christian Bible. You see it enacted in Judeo-Christian history from the Deuteronomic code (“show no mercy”) to Oliver Cromwell’s Puritan genocides. I won’t cite the current examples, but they are all too obvious.
It’s called a ‘dilemma,’ but for two great figures of Western Civilization, there was no dilemma. Socrates counters the fickle, violent gods of the Homeric pantheon with the complete conviction that God is one and God is good. Period. And Christ fulfills this vision by revealing that God is triune love. Period. To them, there was no dilemma. There was simply the Good / Loving God vis-a-vis idols, which were no gods at all. “In him is light, and there is no darkness at all.”
Trinitarian theology roots that love right within the Godhead and proclaims that love as incarnate in Jesus Christ. Christ is the mediator of love who lives his love through us. This exceeds what George P. Grant called ‘bare monotheism.’ In any religion of bare monotheism, God is not normally known as love by nature. Any theology that rejects God as all-merciful and Christ as his mediator will assign its followers the role of God’s direct agents rather than participants in God’s love. Note: this applies to individuals but is also central to nationalism.
At that point, Euthyphro’s dilemma is played out in us. Is my will good because I will it (in God’s name)? Or is my will subject to God’s will-to-love as revealed in Christ? Unfortunately, sometimes Christians prooftext Bible verses, such as “Our God is in heaven; he does whatever pleases him” (Psalm 115:3) as if this reflected God’s self-will rather than anticipating God’s self-revelation in Christ.
So, yes, I think the ethical implications of a robust doctrine of Trinitarian Love are enormous, and spelled out explicitly in Christ’s teachings (a la the Sermon on the Mount) and actions (most clearly on the Cross). These are not, as one author says, ‘afterthoughts’ with God — self-giving love is the deepest truth of who God is and thus, the central ethic of what “participation in the divine nature” means.
In my children’s book, Jesus Showed Us! this is the major theme. “What is God like? Jesus showed us! God is love!” Can we infer an ethic there? No need to infer; it’s spelled out plainly:
“I tell you, love your enemies and pray for those who persecute you, that you may be children of your Father in heaven.” (Matthew 5:44-45).