"Unity in purpose" is the way I've heard it put for LDS. But so do the boy scouts, so this isn't unity as in monotheism. You have God the Father having a simple location. And you have three gods.
This is polythesim.
And, it's a very immature theology. Gods on planets, etc. This is the stuff of early paganism. Zeus and Thor aside, you have multiple Gods existing at a definite location up there in the sky/universe. This is the stuff of primitive societies, a childish view left behind by Judaism millennia ago. You are pre-Judaic in theology.
I think LDS has a ways to go to even begin to understand monotheism, much less the Holy Trinity.
I would be interested in knowing what your thoughts and perspectives on the scriptures cited previously: whole chapter of John 17 (ONENESS of Godhead with Apostles and with followers of Christ), Rom. 8:17 (joint-heirs with Christ), and John 10:34/Psalms 82:6 (Ye are gods)?
The fact that Jesus is the Heir indicates that He is a distinct person and will continue to exist as a person for Eternity. If Jesus and God the Father were of the same substance (or same entity), then it would not make sense for Jesus to proclaim that He came to do the Will of the Father (John 6:38).
What does it mean to you that we were created in the IMAGE of God? It is recorded in scripture that a number of prophets have talked with God “face to face” which indicates that God has an anthropomorphic appearance. Also, it is recorded that God has feelings and passions and determination, which is further evidence of the Personhood for each member of the Godhead.