Peter again quotes one of David's Psalms. David is not speaking of himself in this Psalm. "The Lord" and "my" refer to God; "my Lord" and "your" refer to Jesus the Messiah.
To sit at God’s “right hand” is an idiom that means that Christ will rule as God, with God’s authority. AT: "You take my position of authority," (See: [[rc://en/ta/man/translate/figs-idiom]]).
This means that God will completely defeat the Messiah's enemies and make them subject to him. AT: "until I make you victorious over all of your enemies" (See: [[rc://en/ta/man/translate/figs-metaphor]])