Question: "Did Constantine change the Sabbath from Saturday to Sunday?"
Answer: In the year 321 A.D., 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 a desire to adopt what the Christians had practiced for nearly two and a half centuries.
It is well documented that the early church adopted Sunday as their day of worship. Acts 20:7 speaks of this, "On the first day of the week we came together to break bread. Paul spoke to the people …" and 1 Corinthians 16:2, "On the first day of every week, each one of you should set aside a sum of money in keeping with his income, saving it up, so that when I come no collections will have to be made." 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 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. Colossians 2:14-17 says, "He canceled the record of the charges against us and took it away by nailing it to the cross. In this way, he disarmed the spiritual rulers and authorities. He shamed them publicly by his victory over them on the cross. So don’t let anyone condemn you for what you eat or drink, or for not celebrating certain holy days or new moon ceremonies or Sabbaths. For these rules are only shadows of the reality yet to come. And Christ himself is that reality.” Also see Romans 14:5-6, "One man considers one day more sacred than another; another man considers every day alike. Each one should be fully convinced in his own mind. He who regards one day as special, does so to the Lord. He who eats meat, eats to the Lord, for he gives thanks to God; and he who abstains, does so to the Lord and gives thanks to God."