Question: "Did Constantine change the Sabbath from Saturday to Sunday?"
Answer: It is not secret knowledge that in 321, Constantine decreed, "On the venerable day of the Sun let the magistrates and people residing in cities rest, and let all workshops be closed" (Codex Justinianus lib. 3, tit. 12, 3; trans. in Philip Schaff, History of the Christian Church, Vol. 3, p. 380, note 1). Constantine seems to have made this change himself and not through the papacy, since the "papacy" had not really come in to being at that time. The papacy grew gradually out of the office of Bishop and for many years this was centered in Rome. In any case, it should be noted that in doing this, Constantine is not changing the Sabbath; he is merely making Sunday the official day of rest for the Roman Empire. His motivation was probably not born out of hatred for the Jews (it's hard to say for sure why Constantine or any historical figure did what they did) but out of adoption of the practice that Christians had already been doing for nearly two and a half centuries.
It is well documented that the early church had adopted Sunday as their day of worship. The book of Acts in chapter 20, verse 7 speaks of this, "On the first day of the week, when we met to break bread, Paul began to speak to the people…" and 1 Corinthians 16:2, "On the first day of the week, each of you should set aside some income and save it to the extent that God has blessed you, so that a collection will not have to be made when I come." These passages indicate that Christians were probably meeting regularly on Sunday (the first day of the week). They did this most likely because Christ rose on the first day of the week. It wasn't until hundreds of years later that the death of Christ became the focal point of Christian worship services. That is not to say they thought it unimportant; but they were primarily concerned with His victory over death, most realized in His resurrection.
It is important to remember that corporate worship with other believers is necessary and part of obedience, but the day that your church body chooses to worship on is not really that significant. The New Testament addresses this in a couple of different passages. See Colossians 2:14-17, "He has destroyed what was against us, a certificate of indebtedness expressed in decrees opposed to us. He has taken it away by nailing it to the cross. Disarming the rulers and authorities, he has made a public disgrace of them, triumphing over them by the cross. Therefore do not let anyone judge you with respect to food or drink, or in the matter of a feast, new moon, or Sabbath days— these are only the shadow of the things to come, but the reality is Christ!"
Also see Romans 14:5-6, "One person regards one day holier than other days, and another regards them all alike. Each must be fully convinced in his own mind. The one who observes the day does it for the Lord. The one who eats, eats for the Lord because he gives thanks to God, and the one who abstains from eating abstains for the Lord, and he gives thanks to God."