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?"