How old are you? (rhetorical question)
My point about the reference to Jesus sitting at the right hand of the father is that it demonstrates two Gods. Two distinct Gods.
Whereas, early Jewish followers of Jesus would never have been able to conceptualize Jesus as "another" God because Jesus and the Jews were strict monotheists. "The Lord thy God is one" for example.
So, many conceived of Jesus as the same as the Father in a different manifestation (Sabellius, modalists, monarchians etc.)
"Trust in the LORD with all your heart and lean not on your own understanding" (Proverbs 3:5)
Christ refuted their theological misconception, by mentioning a psalm:
41 While the Pharisees were gathered together, Jesus asked them, 42 saying, “What do you think about the Christ? Whose Son is He?”
They said to Him, “ The Son of David.”
43 He said to them, “How then does David in the Spirit call Him ‘Lord,’ saying:
44 ‘ The LORD said to my Lord,
“ Sit at My right hand,
Till I make Your enemies Your footstool”’?
45 If David then calls Him ‘Lord,’ how is He his Son?” 46 And no one was able to answer Him a word, nor from that day on did anyone dare question Him anymore.
In other words, Christ must be God, and that there is a distinction that can be understood between the Father and the Son. It doesn't make sense that God talks to Himself.
In addition, this is a mystery. We indeed believe in One God. But to describe the one God in the way you like to explain it means you are leaning on your own understanding, and not on divine revelation through the enlightenment of the Holy Spirit (who enlightens the Church and the Scriptures).
"I and the Father are one" John 10:30.
"He who has seen Me has seen the Father" John 14:9
"I am the true vine and my Father is the vinedresser." John 15:1
These are how we understand the Oneness of God. Christ did not say, "I am the Father." Christ did not say, "I am both the vine and the vinedresser." Christ did not pray to Himself. But in a mysterious fashion, He and the Father are One because they are One God, and no one but God truly understands this. We can only give analogies for our weak human minds to fathom it. For instance, the sun has an orb, light, and heat. So is the Father, the Son, and the Holy Spirit. Distinct, but one sun. When a blind man feels the heat, he can say, "This is the sun warming me." If a man sees rays of light shining into the world through the light, one can say, "The sun reveals the world to me." When one looks at a circular object that cannot be seen directly, one knows the sun is there, from which the light is begotten from it, and the heat proceeds from it.
We do not however say the Father is part of God. The Father is God. The Son is God, and the Holy Spirit is God. But the Father is not the Son, and they're both not the Holy Spirit. This is the real mystery of the oneness of God. It is not a simple understanding. It is just as complex as imagining fully four or five dimensional shapes with your mind's eye. We may only see a sliver of understanding, but we will never really understand the Godhead fully except God alone. Polytheism believes in gods who are limited in scope and divinity completely. Other Monotheistic religions believe in gods who are either mere forces or mere persons that send angels to have relationship with us.
When we say "persons" it is the weakness of human language in the way we describe the distinction in the Godhead. Nevertheless, it is a term used to describe how we can have a relationship with God, since we are persons and we want an intimate personal relationship. In addition, when we have a relationship with one person, we don't really see "love" or "intimacy" or "compassion" between the two of us. It becomes a force between two persons. But the Trinity reveals in clear distinction how we can be engrafted into God with the perfection of "persons". The Word of God became man so that in man receiving the Word's own Holy Spirit enlivening him just as it eternally enlivens the Word, we, even in our human state, may become sons of the Father and partake of Divine life. This intimacy does not exist in a one-to-one human basis. Therefore, because of the uniqueness of the Godhead, there should be no comparison, and one should not think of two or three "Gods."