Relational views of God want to describe God as having "real" feelings and emotions. And by "real" they mean "the way we humans have feelings." Trouble is, human feelings are reactive. And while that reactivity feels dynamic and alive--"I do X and God is happy with me"--it releases God's anger, wrath, and hate into the world--"I do Y and God's wrath burns against me." Oddly, this is the very outcome relational views were designed to avoid. Relational views pull off this trick by implicitly delimiting God's emotions to the positive. Yes, God is emotional, but he doesn't have negative emotions. God loves you, always and eternally. So, you don't have to crouch in fear before an emotionally unpredictable and volatile deity.
Notice, again, what is happening here. By restricting God's emotions to the loving and good, and removing any sort of unpredictability and volatility from that goodness and love, relational views have made an argument for God's impassivity. God actually doesn't have emotional reactions like humans do, triggered and provoked as we are. Rather, God is constant oceanic love. Still, unperturbed, peaceful, and generous. This is what the Hebrews described as God's hesed, his unchanging kindness and fidelity. My favorite description of God's impassivity comes from Jesus: "God is kind to everyone. He causes the sun to shine on everyone, both good people and bad people. He also causes the rain to fall on everyone, people who obey him and people who do not obey him." Like sunlight and rain, God's love falls impassively upon the good and the evil. God is not provoked or angered by human sin. As Julian of Norwich said when looking into the heart of God, "I saw no wrath there."
In my opinion, all the trouble we have here boils down to branding. The word "impassive" is just awful. It highlights the wrong thing. "Impassive" is addressing concerns that God can be triggered and provoked. These were ancient Neoplatonic concerns, the worry that God might be "affected" by the world. But a non-reactive and unaffected God appears to us cold and remote. Thus the rise of "relational views" of God which try to infuse some responsivity back into that of view God. But all this is missing the critical issue. By focusing upon the changeability and variability of God's emotions we've taken our eyes off of the valance and quality of God's emotions. Simply put, the word "impassive" doesn't capture the truth that God is love, which is the most important thing you need to say about God's "emotions." By turning us away from God's love, the word "impassive" pictures God as emotionally inert and blank, and then suggests this inertness and blankness never changes. Which just isn't an accurate depiction of God at all, and the relational theologies are right to push against it.
To avoid such confusion, whenever in my writing I use the word "impassive" I use it in relation to human sin. For example, I'll write, "God is impassive toward human sin." That is to say, God is not provoked or angered by our sin. God isn't triggered by our moral failures. This use of the word "impassive" allows us to see where classical theism and the relational theologies find common ground. Further, such a use of the word "impassive" avoids describing God as emotional inert, cold, and distant. Rather, God is constant unchanging love no matter what we do. Instead of "I do X and God is happy" or "I do Y and God is wrathful" it is "I do X and God is loving" and "I do Y and God is loving." Or, as Jesus said, "God is kind to everyone."
If I were going to offer my correction to the relational views about God, this is what I'd suggest. God is a relational God because God is Person, not a person, but Person Itself. And we, as little persons, are made in the image and likeness of God. What makes God relational isn't emotionality but this exchange between persons, the I-Thou address between God and myself. God responds to us because God is Person, not because God is emotionally provoked, triggered, or reactive toward our actions. Rather, God is Love, unchanging and eternal.
That's my take. When you say "God is impassive" you mean "God is love."