How is Jesus' will in union with the Father's? (Catholic perspective) I and the Father are one. (John 10:30)
that all of them may be one, Father, just as you are in me and I am in
you. May they also be in us so that the world may believe that you
have sent me. (John 17:21)
Father, if you are willing, take this cup from me; yet not my will,
but yours be done. (Luke 22:42)

In Luke we can see that Jesus' will was or could be different from the Father's. According to the Catholic Church, in what sense is Jesus' will united (the same) with that of God the Father? Or what is the Catholic interpretation regarding Jesus' remark, &quot;yet not my will&quot; if their will is fully united?
This is the question dealt with by the Sixth Ecumenical Council (the Third Council of Constantinople). The council addressed the heresy known as monothelitism. The heresy held that Jesus Christ only had one will.

The orthodox position was defined at that Council: Jesus Christ had two natures, human and divine; he also had two wills, human and divine. If there was no human will in Christ, the Incarnation would have been incomplete, as he would not have adopted everything that belongs to humanity (cf. Gregory of Nazianzus: "What is not assumed is not healed"). This is the logical outworking of Chalcedonian Christology (the idea that Christ is both human and divine).

The Catholic (and Orthodox, and Protestant) position is that the "not my will, but yours, be done" refers to the human will in Christ.

This is dealt with directly in the writings of Maximus the Confessor (I will try to find the citation), indirectly in the definition of the Sixth Council, and directly several times in the Summa Theologica of S. Thomas Aquinas (third part, question 18).