On the Patrick Coffin show, Catholic Answers Live, their guest was asked about the impassibility of God.
The Problem: If our response to God doesn't make God happier, then He doesn't really love us or care for us.
There's some mystery here, not of darkness, but of light--too much light. Conflicting principles. Some kind of anthropomorphizing of God. For us to act, or when we act to do good for another, it does make us happy when we succeed. We act in order to be happy.
We are like God, but God is not like us. There is no "need," no "reason" in that sense, for Him to love us. His love is utterly gratuitous. He does truly know us and love us and desire our salvation, and I think He does take delight in His people (story of the Prodigal Father), but His joy is not our kind of joy and His feelings are not our kind of feelings.
God is not changed by the change in our behavior. We are changed by fulfilling His will. He is not.
We do not have any good model of impassibility. There is nothing like it in our lives (except dumb rocks over the short run, I suppose).
Though we know some truths abstractly about God's eternity, it is better to picture Him partying with His beloved children. Changeless does not mean "immobile," like a statue or a rock or a mountain. God can breath, and speak, and act, and dance, without ever ceasing to be the eternal God. Our actions resemble His, but His actions do not resemble ours. It is not a reduction of potency to act in Him, for He is pure act. But He has he freedom to act, both within the Trinitarian relations and in our lives.