I know God accepted Jesus's sacrifice as a propitiation for our sins, but the part that stumps me is that Jesus only had to die physically. He didn't experience eternal separation from God as I would. Jesus only went to Hell for 3 days, so who is serving my "life sentence" in Hell if Jesus is now sitting at the right hand of the Father?
Jesus' time in the grave was not a payment for our sin or the reason we avoid eternity in Hell. As the question points out, Jesus was dead for only three days, yet God's word decrees an eternal death (i.e., separation from God) for any who reject Christ and die in sin. In reality, Jesus' time spent in the grave served an entirely different purpose in God's plan.
First, the wording of the question assumes that "spending eternity in hell" is similar to serving time in prison for a crime. Such a comparison falls short of explaining why the unjust are sent to the Lake of Fire. To know Hell's true purpose, we must begin by understanding what Jesus' death accomplished on our behalf.
When Adam was instructed not to eat of the fruit of the Tree of Knowledge of Good and Evil, God promised that if he disobeyed, Adam would die. Later in Revelation 20:14 we learn that the death God was speaking about in Genesis is the "second" death, which is an eternity spent in the Lake of Fire. This is God's promised outcome for sin. It is not a period of restitution or "paying off our debt." Rather, it is the future existence God decreed for any who disobey His word.
Secondly, Scripture says that God's perfect character must display wrath against unholiness, and, therefore, our very sinful nature demands that we receive God's wrath. Men remain subject to His wrath for as long as they exist in sin, and those who die in their sins without placing their trust in Jesus Christ remain eternally sinful. Therefore, they remain eternally subject to God's wrath because the sin nature of the unbeliever follows them into the grave. They must live forever in Hell (and later the Lake of Fire) because there is no solution to their sin if they reject Christ.
Jesus Christ addressed both these issues on our behalf by His sinless life and sacrificial death on the cross. First, Jesus lived a perfect, sinless life. He had no sin of His own, scripture says. Since He lived a sinless life, Jesus did not warrant God's wrath nor did He deserve death. Therefore, His perfect life is available for God to credit to us by faith. When we believe in the God's word, we are given Christ's righteousness. Paul expresses it this way:
So, believers in Jesus Christ are made righteous by our faith. We have "put on" Christ, Paul says in Romans 13:14, meaning we are covered in His righteousness, which was given to us by the Father through faith in Christ. Therefore, we enter Heaven because we are righteous by faith.
Secondly, Jesus's death on the cross gave an opportunity for God's wrath to be satisfied for sin. Though we deserved God's wrath for our sin, Jesus took God's wrath on our behalf. His death on the cross was the moment God's wrath for sin was poured out on Jesus, as He became our propitiation or payment.
Take note that God's wrath for sin was satisfied in the death of Christ alone. God's did not require that Jesus spend time in Hell to satisfy His wrath because as we said earlier, the Second Death is not a "payment" to satisfy God's wrath. It is the dwelling place assigned to those who exist in sin eternally. Since Jesus had no sin of His own, He had no reason to live in Hell (or the Lake of Fire) forever.
Therefore, believers avoid eternal death not because Jesus took our place in Hell; we escape that punishment because by our faith in Christ we become eligible to live in Heaven. Our entrance into Heaven requires both a payment for our sins and we being made righteousness. Christ accomplished both for us by His life and death. By Christ's sinless life, we have been credited with Christ's righteousness, and by Christ's death on the cross, God's wrath for our sin has been appeased.
So why did Jesus spend three days in the grave after He died?
First, Jesus spent three days in the grave to prove He was the Messiah, risen from the dead in fulfillment of scripture:
Jesus remain dead for three days to fulfill scripture and to demonstrate He was the Messiah. The three-day period Jesus spent in the grave precluded anyone charging Jesus "faked" His death. Three days was enough time to establish beyond any doubt that Jesus was truly dead so that when He resurrected, everyone could know He kept His promise to abolish death.
Secondly, Jesus used His time in the grave to preach to those in Sheol, the holding place of the dead prior to the resurrection. Sheol is two parts: Abraham's Bosom and Hades. You can read about these two places in Luke 16.
Prior to Christ's death and resurrection, Old Testament saints (i.e., believers ) who died were unable to enter Heaven. Though they were righteous by their faith even before Christ's death on the cross (e.g., Romans 4:9), until Jesus blood was spilled, God's wrath had not been satisfied. Therefore, the Lord made a place of comfort for OT saints to wait until the Lord's coming.
After His death, Jesus descended into Sheol, to Abraham's Bosom, which is the side of Sheol reserved for the saints. It is not a place or torment. Jesus never experienced "Hell" or torment during the time He was in the grave. Instead, Peter says that Jesus used the three days in the grave to "preach" to the Old Testament saints and to the unbelievers held in the other side of Sheol, Hades, which is a prison for unbelivers as they await their judgment day: