Why is Jesus sitting at "God’s right hand" not "the Father's right hand"?

Accept the following as a possible explanation, not necessarily a Biblical exposition.

If you were a two dimensional being living on a 2D plane, and I was a three dimensional being in a 3D plane and I had the ability to make you see into 3D while pointing my hand with its fingers towards you, this is likely what you would see:

Keep in mind 2D characters can only see in 1D lines.

You are seeing my thumb on the right-hand of my hand while it is absolutely one with the whole. The perceived unconnectedness is only the result of your limited ability to see reality. The thumb is one with the hand.

I am not suggesting this as an analogy but a parable: I'm not saying God is like the hand and Jesus is the thumb, but rather like this is a reasonable explanation for the apparent unconnectedness of the thumb and hand, a similar reason might exist why we are incapable of perceiving how Jesus can be at the right hand of God while actually being indivisibly part of the Triune God.

Could it be, that a natural person with his 3-dimensionally trained mind, fed with input from his 2-dimensional vision, seeing into the spiritual realm where Jesus is seated (who knows in what dimension), is completely incapable of expressing with the limitations of language, the full truth of what is in view? Jesus is maybe not at the right of the Father but at the right hand of the Triune God of Whom He is indivisibly One with - our limited ability to perceive how that is possible does not challenge the doctrine of the Trinity but just exposes how little we actually can perceive and understand of the realm that God inhabits.

Since we believe the one God, Yahweh, is triune, "Father, Son, and Holy Spirit" (Matthew 28:19), to refer to any of the persons by simply the word "God," in an unqualified manner is perfectly valid, and even natural.

That is to say, we can mean, for example, "the Son" by 'God' in the phrase "the blood of [God]" (Acts 20:28) without referring explicitly to the Son, of whom it is obviously said, and God understood. Likewise, when St. Peter calls the Holy Spirit "God," but doesn't explicitly say the Holy Spirit, we know that the Holy Spirit is the immediate appositional referent.

"But Peter said: Ananias, why hath Satan tempted thy heart, that thou shouldst lie to the Holy Ghost, and by fraud keep part of the price of the land? Whilst it remained, did it not remain to thee? and after it was sold, was it not in thy power? Why hast thou conceived this thing in thy heart? Thou hast not lied to men, but to God. (Acts 5:3-4).

In other words, we rely on context to indicate either which or whether any person in particular is meant by the word.

In John 1, for example, when we hear that God created the world and the Word was He through Whom He made the world, that the first instance of "God" refers to the Father, and the latter to the Son, because the Word is the Son of God, and because of the impossibility of the Father, who is the head of the Trinity (as well as the Spirit who is part of the Trinity) of being excluded from creation where we know the Son was.

Likewise, in the Old Testament, the Messenger of Yahweh, a mysterious figure who is sent from God, yet is identified as Yahweh himself and himself says he is Yahweh, and is identified as the Saviour. The Fathers of the Church understood this Messenger of the Lord to be Christ before His incarnation, and not an angelic being. He speaks of God in the third person in the same breath as he says that He is Yahweh, where it is therefore understood to refer to the Father.

So when Jesus is stood on the right side of God, it can only refer to the Father, and so no more specificity is required. In fact, in the New Testament period, to call the Son or Spirit "God" was we do today was a rarity. Instead, in the primitive period in the Church, the Son and Spirit were viewed of with respect to the Father: 'God because from God.' Rather than God 'alongside' the Father as some equally Father-like person, simply because He is co-eternal, or as if there was no actual distinction between the persons. That is, "God from God, Light from Light, true God from true God" (Nicene Creed). Even in the Nicene Creed, God is used of the Father here because He is, according to orthodox trinitarian theology, the Source of the Son and the Spirit (meant with respect to relationship - eternal begetting, or eternal proceeding from, not temporality).

For this to be in conflict with the doctrine of the trinity, instances where we do see the Father specified instead of simply saying "God," would have to also conflict with a denial of the Trinity.