Yes, Satan did want Jesus to be crucified.
But it is significant to note that he didn’t want it for the same reasons as those he used as tools did. As the ultimate betrayer, Satan made it look to others like serving Satan’s interests was serving their own.
Judas wanted money (see Luke 22:5-6). He may have wanted fame too. His additional motives have been explored in a variety of ways (I asked a question about this here). My personal view, however, is that whatever else may have occurred to Judas, his principal motivation was greed. From John 12:
5 Why was not this ointment sold for three hundred pence, and given to
6 This he said, not that he cared for the poor; but because he was a
thief, and had the bag, and bare what was put therein.
The Sanhedrin (or at least many members thereof) was:
- Envious of Jesus’ popularity (see Matthew 27:18 & discussion on this
- They saw Him as a risk to their power (see John 11:47-53)
- They did not like His teachings, such as:
13 But woe unto you, scribes and Pharisees, hypocrites! for ye shut up
the kingdom of heaven against men: for ye neither go in yourselves,
neither suffer ye them that are entering to go in.
14 Woe unto you, scribes and Pharisees, hypocrites! for ye devour
widows’ houses, and for a pretence make long prayer: therefore ye
shall receive the greater damnation. (Matthew 23:13-14)
They wanted Jesus out of the way and thought that by killing Him they would succeed. In particular, having Him publicly killed by the Romans would be especially excruciating and humiliating, and it would (they thought) scare off His followers by showing them that Jesus was an enemy to Rome.
Peter did not want Jesus crucified. I suggest that Satan’s temptation of Peter noted in the OP, while it may have been designed by Satan to play on Jesus’ love for His closest disciples, was particularly geared towards tearing down Peter himself. As noted by Jesus:
Simon, Simon, behold, Satan hath desired to have you, that he may sift
you as wheat: (Luke 22:31)
Satan would have loved to see Peter:
- Lose faith in Jesus and apostatize OR
- Go all the way the other direction and get himself killed at the same
time as Jesus
But of course Satan was attacking Jesus at the same time. Like Dumbledore's trust in Snape (over and against the arrogant blindness of Voldemort), Jesus knew who Peter was and what he would ultimately be able to do:
But I have prayed for thee, that thy faith fail not: (Luke 22:32)
The architect of the treachery here wanted Jesus to be crucified for a very different reason. As noted in other responses, Satan wanted Jesus to fail as Savior. Satan knew full well who Jesus was.
From Satan’s followers:
And, behold, they cried out, saying, What have we to do with thee,
Jesus, thou Son of God? art thou come hither to torment us before the
time? (Mathew 8:29)
And the great insight by James:
Thou believest that there is one God; thou doest well: the devils also
believe, and tremble. (James 2:19)
Satan’s goal hadn’t really changed since before he was cast out of heaven. Understanding Isaiah 14 to teach about Satan through the allegory of the King of Babylon:
6 He who smote the people in wrath with a continual stroke, he that
ruled the nations in anger, is persecuted, and none hindereth. …
How art thou fallen from heaven, O Lucifer, son of the morning! how
art thou cut down to the ground, which didst weaken the nations!
13 For thou hast said in thine heart, I will ascend into heaven, I
will exalt my throne above the stars of God: I will sit also upon the
mount of the congregation, in the sides of the north:
14 I will ascend above the heights of the clouds; I will be like the
most High. …
27 For the Lord of hosts hath purposed, and who shall
disannul it? and his hand is stretched out, and who shall turn it
Satan wanted to disannul God’s purposes and make Him fail in His word. Satan wanted to rule, to smite people down, he wanted the glory and the power, he wanted to be better than everyone else—and he thought he could outsmart God.
What ultimately was Satan hoping to accomplish through the betrayal of Judas, the envy of the Sanhedrin, and the misplaced devotion of Peter? Luke understood:
And the people stood beholding. And the rulers also with them derided
him, saying, He saved others; let him save himself, if he be
Christ, the chosen of God. (Luke 23:35)
Talmage put it poignantly well:
The dominant note in all the railings and revilings, the ribaldry and
mockery, with which the patient and submissive Christ was assailed
while He hung, ‘lifted up’ as He had said He would be, was that awful
‘If’ hurled at Him by the devil’s emissaries in the time of mortal
agony; as in the season of the temptations immediately after His
baptism it had been most insidiously pressed upon Him by the devil
himself. That ‘If’ was Satan’s last shaft, keenly barbed and doubly
envenomed, and it sped as with the fierce hiss of a viper. Was it
possible in this the final and most dreadful stage of Christ’s
mission, to make Him doubt His divine Sonship, or, failing such, to
taunt or anger the dying Savior into the use of His superhuman powers
for personal relief or as an act of vengeance upon His tormentors? To
achieve such a victory was Satan’s desperate purpose. (Jesus the Christ pp. 658-659)
Satan wanted Jesus to be crucified so he could put Him in that terrible, tempting situation--in hopes of getting Him to do something that would disqualify Him from His perfect salvific role.
Satan, like the supervillains of literature, didn’t let his minions in on his master plan—he much preferred they didn’t see the big picture. Jesus was open about His mission and brought people to see.
Satan wanted to disrupt the plan of God by getting Jesus to fail in His mission. There was only one Christ (the Anointed One); there was no backup Savior. God gave His Only Begotten Son. The atonement of Christ was the showdown between the Greatest that God sent and the worst Satan could muster. Satan was blinded by his arrogance then as he was before; God had Satan beat since before the foundation of the world.
The plan of salvation was anchored in faith from the very beginning—the Father trusted the Son and knew Him well enough to know He would not fail.