But you cannot answer whether the Father's happiness consists of/is dependent on the Son, and vice versa?
Piper offers the following (
The Pleasures of God):
“…the Gospel is the good news that God is the all-satisfying end of all our longings, and that even though he does not need us, and is in fact estranged form us because of our God-belittling sins, he has, in the great love with which he loved us, made a way for sinners to drink at the river of his delights through Jesus Christ. And we will not be enthralled by this good news unless we feel that he was not obliged to do this. He was not coerced or constrained by our value. He is the center of the gospel. The exaltation of his glory is the driving force of the gospel. The gospel is a gospel of grace! And grace is the pleasure of God to magnify the worth of God by giving sinners the right and the power to delight in God without obscuring the glory of God.
The Scriptures speak of God’s delight (joy, happiness) in His Son (e.g., Matthew 17:5; John 3:35; John 10:17; John 17:24-26 and more). God’s pleasure in His Son is actually pleasure in Himself. The Son is the image of God, equal with God, in fact is God, thus the delight God feels for His son is a delight in Himself. We read in 2 Corinthians 4:6, “…the glory of God in the face of Jesus Christ.” From eternity in the face of His Son God has beheld the panorama of His own perfections and rejoices with infinite joy in this.
Is this vanity?
It would be vanity if our deepest joys were found looking in a mirror. We would be smug and conceited if we imitated God like this. While we are to imitate God (see Matthew 5:48; Ephesians 5:1), we are not to imitate Him in every way. Adam wanted to imitate God, to be like God in a manner that was never intended—to be self-reliant. But only God is self-reliant—we should be God-reliant. We were not created for self-contemplation, rather something greater and far more nobler—for the “contemplation and enjoyment of God!” Indeed, anything less is idolatry toward God and ultimately disappointment for ourselves. The most glorious of all beings is God and to not love and delight in Him is a tremendous loss to us and an insult to God.
How shall God not insult what is infinitely beautiful and glorious? How shall God not commit idolatry? There is only one possible answer. God must love and delight in his own beauty and perfection above all things. For us to do this in front of the mirror is the essence of vanity; for God to do it in front of his Son is the essence of righteousness.