Yes, there is conflict of wills, which is why Jesus suffered, in addition to the physical suffering. In the previous post was the answer that the suffering was “obedience unto death” which means obedience of the human will to the divine will.
The Catechism of the Catholic Church give more detail:
612 The cup of the New Covenant, which Jesus anticipated when he offered himself at the Last Supper, is afterwards accepted by him from his Father’s hands in his agony in the garden at Gethsemani,434 making himself “obedient unto death”. Jesus prays: "My Father, if it be possible, let this cup pass from me. . ."435 Thus he expresses the horror that death represented for his human nature. Like ours, his human nature is destined for eternal life; but unlike ours, it is perfectly exempt from sin, the cause of death.436 Above all, his human nature has been assumed by the divine person of the “Author of life”, the “Living One”.437 By accepting in his human will that the Father’s will be done, he accepts his death as redemptive, for "he himself bore our sins in his body on the tree."438
Christ’s death is the unique and definitive sacrifice
613 Christ’s death is both the Paschal sacrifice that accomplishes the definitive redemption of men, through “the Lamb of God, who takes away the sin of the world”,439 and the sacrifice of the New Covenant, which restores man to communion with God by reconciling him to God through the “blood of the covenant, which was poured out for many for the forgiveness of sins”.440
614 This sacrifice of Christ is unique; it completes and surpasses all other sacrifices.441 First, it is a gift from God the Father himself, for the Father handed his Son over to sinners in order to reconcile us with himself. At the same time it is the offering of the Son of God made man, who in freedom and love offered his life to his Father through the Holy Spirit in reparation for our disobedience.442
In the Gospels we read of the passion before the crucifixion:
The Agony in the Garden. Matthew 26:36-46:
Then Jesus came with them to a place called Gethsemane, and he said to his disciples,
“Sit here while I go over there and pray.”
He took along Peter and the two sons of Zebedee, and began to feel sorrow and distress. Then he said to them, “My soul is sorrowful even to death. Remain here and keep watch with me.”
He advanced a little and fell prostrate in prayer, saying, “My Father, if it is possible, let this cup pass from me; yet, not as I will, but as you will.”
When he returned to his disciples he found them asleep. He said to Peter, “So you could not keep watch with me for one hour? Watch and pray that you may not undergo the test. The spirit is willing, but the flesh is weak.” Withdrawing a second time, he prayed again, “My Father, if it is not possible that this cup pass without my drinking it, your will be done!” Then he returned once more and found them asleep, for they could not keep their eyes open. He left them and withdrew again and prayed a third time, saying the same thing again. Then he returned to his disciples and said to them, “Are you still sleeping and taking your rest? Behold, the hour is at hand when the Son of Man is to be handed over to sinners. Get up, let us go. Look, my betrayer is at hand.”
