Jesus sits at the right hand of God because the throne is God's.
The Book of Revelation clearly distinguishes between the Almighty God, “Him who sits on the throne” (Revelation 4) and “the Lamb standing, as though it had been slain” (Revelation 5). The two are never confused. The Lamb is not God (who sits on the throne), God is not the Lamb. The God of chapter 4 is worshiped because He is God who created everything.
We can all agree that “the Lamb, standing as though it had been slain” in the Book of Revelation 5:6 is Jesus the Messiah, who was killed, but then raised from the dead. God, on the other hand, does not die, and is not raised from the dead.
Note how the Lamb is continually differentiated from God, who sits on the throne. That is, God is not the Lamb, and the Lamb is not God:
“To Him who sits on the throne and to the Lamb be blessing and honor and glory and might forever and ever!”.– Rev. 5:13
"Fall on us and hide us from the face of Him who is seated on the throne, and from the wrath of the Lamb”.Rev. 6:16
After this I looked, and behold, a great multitude that no one could number…standing before the throne and before the Lamb, clothed in white robes, with palm branches in their hands.– Rev. 7:
“…crying out with a loud voice, “Salvation belongs to our God who sits on the throne, and to the Lamb!”– Rev. 7:10
The same distinction between God, on the one hand, and the Lamb on the other, is made in Revelation 7:17, 14:4, 15:3, 21:22, 21:23, 22:1 and 22:3. In many other places in the Book of Revelation, Jesus Christ and the symbols representing Jesus Christ are differentiated from God (e.g., Rev. 11:15, 12:5).
The last two references to God and the Lamb in the Book of Revelation (Rev. 22:1 and 22:3) contain the phrase “the throne of God and of the Lamb”. Some Trinitarians claim that this phrase shows that the Lamb is God. But this assumption is wrong for several reasons:
In these verses as well, God is distinguished from the Lamb. Whoever God is, He is not the Lamb. The Lamb is not God, and God is not the Lamb. The Lamb was slain and raised. God is not slain and raised.
This incorrect interpretation ignores all the other references in the Book of Revelation which also differentiate between God and the Lamb, and which state that the Lamb has a God.
The Lamb shares the throne of God because God has granted this to the Lamb: “he shall rule…even as I myself have received power from my Father (Rev. 2:27, 3:21, cf. Matt. 28:18). As a parallel, the LORD God put both David and Solomon on His (God’s) throne. “Then Solomon sat on the throne of the LORD as king in place of David his father” (1 Chron. 29:23). But neither David nor Solomon were God just because they were granted by God to rule as God’s representatives on God’s throne. As God’s chosen, anointed kings, David and Solomon were granted to sit on God’s throne. So is the risen Jesus Christ.
It is clear from the Book of Revelation that Jesus Christ, the Lamb who was slain but who now lives, the firstborn from the dead, the beginning of God’s creation, is not God.
Sometimes Trinitarians say that the deity of Christ was revealed to the apostles gradually or progressively. If that were the case, we should expect to find Jesus clearly presented as God in the Book of Revelation, the last book of the New Testament canon. Yet that is not the case. Instead, the Book of Revelation distinguishes between God and Jesus. Revelation tells us that God is not Jesus and Jesus is not God.
It is apparent throughout the NT that Christ, before and after his resurrection, is shown to be distinct from God the Father. John 5:44 (only means monou, Strong's Greek 3441: Only, solitary, desolate. God") Jesus' language here is explicit as it is elsewhere. In John 17:3 ASV (And this is life eternal, that they should know thee the only true God, and him whom thou didst send, even Jesus Christ) two persons are distinguished, one inferior to the other. "Throughout Paul's epistles ...this distinction is carefully observed, (1 Timothy 2:5 ASV For there is one God, one mediator also between God and men, himself man, Christ Jesus) in which one being alone is always called God (Adonai), the other, without exception, lord (Adoni) ...Again, Christ is expressly declared to be inferior and subordinate to God the Father. He himself said: "My Father ...is greater than all" (John 10:29) and yet more precisely, "My Father is greater than I (John 14:28). He is said to be "chosen," "appointed," "inspired," "sanctified," by God; "anointed," "given," Matthew 12:18; Luke 4:18; John 3:34 and thirty-five times in St. John's Gospel alone, "sent" by God. It is recorded that he came to do his Father's will—came in the name of the Lord. John 4:34; 12:49; 6:38; Matthew 21:9. In St. Matthew's Gospel he is called the "servant of God." Matthew 12:18. Surely, the being that is chosen, appointed, sent, inspired, sanctified, who comes in the name of the Lord, and is God's servant, etc., cannot be said to be equal to his master.
Even after his exaltation, Matthew 28:18 to the right hand of God, Acts 5:31, he is still subordinate. He now reigns in the heavenlies, but soon he will return on the clouds in power and glory to establish God's Kingdom on this earth for a thousand years. After the thousand years he will still be seen to be subordinate to God the father and be subject to Him, 1 Corinthians 15:27-28 for he will return the kingdom to the Father. "Then comes the end, when he delivers the kingdom to God the Father after destroying every rule and every authority and power. For he must reign until he has put all his enemies under his feet. The last enemy to be destroyed is death. For 'God has put all things in subjection under his feet.' But when it says, 'all things are put in subjection,' it is plain that he is excepted who put all things in subjection under him. When all things are subjected to him, then the Son himself will also be subjected to him who put all things in subjection under him, that God may be all in all" (ESV).
Your question "How does this coincide with the doctrine of the trinity?"
"...the Trinity is 'an unintelligible proposition of Platonic mysticisms that three are one and one is three; and yet one is not three and three are not one."
"There is no passage of Scripture which asserts that God is three. No authentic verse claims that the One God is three persons, three spirits, three divine, infinite minds, or three anything. No verse or word of the Bible can be shown to carry the meaning 'God in three Persons.' Any claim that there are three who compose the deity must be based on inference, rather than plain statements.
If some believe that Jesus is God, why wouldn't they believe him when he said that the Father is the only true God, John 17:3; 5:44 that the Father is greater than him, John 14:28. Jesus has a God, John 20:17. Jesus ascribed creation to God, not himself, Mark 10:6 YLT (but from the beginning of the creation, a male and a female God did make them) In Jesus' plain and unequivocal statements, he is not the only true God and Creator. His God is.