Peace can come from time to time when we experience an outpouring of the Spirit. However, the peace Jesus promises is rest in the Lord, which refers to the state one attains when their calling and election is made sure.
Now for the secret and grand key. Though they might hear the voice of God and know
that Jesus was the Son of God, this would be no evidence that their election and calling was made sure, that they had part with Christ, and were joint heir with him. They then would want that more sure word of prophecy, that they were sealed in the heavens and had the promise of eternal life in the kingdom of God. Then, having this promise sealed unto them, it was an anchor to the soul, sure and steadfast. Though the thunders might roll and lightnings flash, and earthquakes bellow, and war gather thick around, yet this hope and knowledge would support the soul in every hour of trial, trouble and tribulation. Then knowledge through our Lord and Savior Jesus Christ is the grand key that unlocks the glories and mysteries of the kingdom of heaven. (TPJS p.298)
Jesus even goes out of his way to tell us that this peace is "not as the world giveth" so as to clue us in to expect the unexpected. And thus we see how Jeremiah could be at peace though he was neck high in a septic tank; how Peter could be at peace though he was being crucified; how Moroni could be at peace though he was hunted by every survivor in the land; how various others could be at peace though sawn asunder, burned at the stake, tried on spurious charges, etc.
God turns up the affliction and temptation knobs as fast as we can handle them. As we increase in favor with God, so he allows us to experience more and greater affliction. Consider the patriarchs and other exalted persons. Without fail, those who were promised eternal life by God were exposed to miserable hardships. These men lived out lonely lives filled with suffering. Yet, Jesus approached near unto them in accordance with their sufferings.
Pause for a moment and consider the last time you were in a great deal of pain. The pain need not be physical--emotional pain is just as effective. How close were you to God before the onset of that pain? And during? There are those who can cry out to God with just as much earnestness outside of suffering as in, but for most of us, this is beyond our current capability. Even Jesus learned obedience by the things he suffered: "Though he were a Son, yet learned he obedience by the things which he suffered;" (Hebrews 5:8)
The only way to approach God is through great suffering. Instead of rejoicing when times are easy, we ought to take careful stock of our lives. God only withholds trials from those who have demonstrated their inability to deal with them.
Salvation is nothing more nor less than to triumph over all our enemies and put them under our feet. And when we have power to put all enemies under our feet in this world, and a knowledge to triumph over all evil spirits in the world to come, then we are saved, as in the case of Jesus, who was to reign until He had put all enemies under His feet, and the last enemy was death. (TPJS p297)
The ideal way to move through life is to be continually increasing the number of situations we have put under our feet. As we do, God will continue to send us as much hardship as we can bear, with temporary breaks as we need them. As he increases the heat, there will likely come a point in a day, week, month, or matter of years, where we hit a situation where we refuse to listen to his voice (mostly represented in our conscience). Note that it is our choice to fail, as he has promised to never send us more than we can handle. We lose some level of light and truth at this point, but if we mount up and take courage, we will eventually be given another opportunity to succeed where we have failed. This process does not have to take much time. If we completely turn over our will to God, as Jesus did, it can be very short indeed. It was a short period for Jesus, as he never withheld his will from God. Jacob and Mormon were both redeemed from the fall in their youth. It need not take a lifetime.
We should not pray to have God remove trials from us. Instead, we should reconcile ourselves to God's will and ask him to bless us with the knowledge we need to overcome our trials.
How does knowledge assist us in overcoming our trials? Temptations and trials have no power over us to the degree that we know and see things as they really are. The more we obey God's word to us on an individual level, the more he can reveal to us. The more he reveals to us, the more truth we comprehend. The more truth we comprehend, the less influence the flesh, money, armies, navies, false priests who oppress, and all other tools of evil are able to entice us. One who knows the end from the beginning cannot be enticed to walk down the wrong path.