The “Sabbath” commandment was changed by man, not by God. Some say the Sabbath command was only for the Israelites (Jews). Why don't we do it?

First of all, let’s start with the commandment God gave concerning the Sabbath: Remember the Sabbath day by keeping it holy. Six days you shall labor and do all your work, but the seventh day is a sabbath to the Lord your God. On it you shall not do any work, neither you, nor your son or daughter, nor your manservant or maidservant, nor your animals, nor the alien within your gates. For in six days the Lord made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy—God speaking, Exodus 20:8-11. Let’s highlight some definitions. The word “Sabbath” comes from the Hebrew word SHABATH (shaw-bath^)—a verb meaning to repose, to rest, to rid of, to still, to put away, to leave. Most often, the word expresses the idea of resting, as in abstaining from labor. This is the word used of God to describe His rest after the completion of creation: By the seventh day God had finished the work he had been doing; so on the seventh day he rested from all his work. And God blessed the seventh day and made it holy, because on it he rested from all the work of creating that he had done—Genesis 2:2-3. It is that same pattern of rest that God then required of His people as one of the ways of living lives pleasing to Him. God practiced what He preached, too; in the wilderness, He provided manna for the nation of Israel, but He did it like this: When the dew was gone, thin flakes like frost on the ground appeared on the desert floor. When the Israelites saw it, they said to each other, “What is it?” For they did not know what it was. Moses said to them, “It is the bread the Lord has given you to eat. This is what the Lord has commanded: ‘Each one is to gather as much as he needs. Take an omer for each person you have in your tent.’” The Israelites did as they were told; some gathered much, some little. And when they measured it by the omer, he who gathered much did not have too much, and he who gathered little did not have too little. Each one had gathered just as much as they needed. Then Moses said to them, “No one is to keep any of it until morning.” However, some of them paid no attention to Moses; they kept part of it until morning, but it was full of maggots and began to smell. So Moses was angry with them. Each morning everyone gathered as much as he needed, and when the sun grew hot, it melted away. On the sixth day, they gathered twice as much—two omers for each person—and the leaders of the community came and reported this to Moses. He said to them, “This is what the Lord commanded: ‘Tomorrow is to be a day of rest, a holy Sabbath to the Lord. So bake what you want to bake and boil what you want to boil. Save whatever is left and keep it until morning.’” So they saved it until morning, as Moses commanded, and it did not stink or get maggots in it. “Eat it today,” Moses said, “because today is a Sabbath to the Lord. You will not find any of it on the ground today. Six days you are to gather it, but on the seventh day, the Sabbath, there will not be any.” Nevertheless, some of the people went out on the seventh day to gather it, but they found none. Then the Lord said to Moses, “How long will you refuse to keep my commands and my instructions? Bear in mind that the Lord has given you the Sabbath; that is why on the sixth day he gives you bread for two days. Everyone is to stay where they are on the seventh day; no one is to go out.” So the people rested on the seventh day—Exodus 16:14-30.
The word “holy” is also noteworthy; in the Hebrew the word is QADASH (kaw-dash^)—a verb meaning to set apart, literally to withdraw someone or something from profane or ordinary use. So the establishment of a Sabbath day was a profound statement by God as to the life pleasing to Him. It was intended to be a day lived out unlike any other day of the week, and consecrated as a perpetual memorial God, a remembrance for (1) His resting following His works of creation, and (2) His miraculous work of rescuing Israel from Egypt; in Moses’ relating God’s commandments in Deuteronomy, he added these words of the Lord’s: Remember that you were slaves in Egypt and that the Lord your God brought you out of there with a mighty hand and an outstretched arm. Therefore the Lord your God has commanded you to observe the Sabbath day—God speaking, Deuteronomy 5:15. God also made clear His intention that the Sabbath always continue to be observed: “Say to the Israelites, ‘You must observe my Sabbaths. This will be a sign between me and you for the generations to come, so you may know that I am the Lord, who makes you holy. Observe the Sabbath, because it is holy to you. Anyone who desecrates it must be put to death; whoever does any work on that day must be cut off from their people. For six days work is to be done, but the seventh day is a Sabbath of rest, holy to the Lord. Whoever does any work on the Sabbath day is to be put to death. The Israelites are to observe the Sabbath, celebrating it for the generations to come as a lasting covenant. It will be a sign between me and the Israelites forever, for in six days the Lord made the heavens and the earth, and on the seventh day he abstained from work and rested’”—God speaking, Exodus 31:13-17. In other words, this commandment has the same rank and substance as do any of the other nine commandments. There is no “statute of limitations” that has somehow run out.
So what happened to change from Saturday (Friday sunset to Saturday sunset) Sabbath to Sunday? Jesus Christ—specifically His resurrection. God’s resurrecting His Son was His certifying to the world that the long-awaited Savior of mankind and paid a completely full and valid price for sin, for sinners, and for the curse of death that sin had brought. When at Christ’s death the curtain in the temple separating the Holy Place from the Holy of Holies was torn apart, graphically signaling an end to the old ways of seeking peace with God, so also the resurrection of Christ signaled an end of an old era and the beginning of a new one—the church. As the church began to emerge and distinguish itself, one of its first “markers” of distinction from Judaism was the separation of Sunday as their holy day of the week. They had both historical and theological reasoning for this: (1) Jesus rose on a Sunday, (2) He appeared on a Sunday—the first Easter Sunday—to Mary Magdalene, the other women, Simon Peter, Cleopas and his companion on the road to Emmaus and, later that same day, to fully 10 of the disciples, (3) a week later, also on a Sunday, he appeared to the disciples to confront Thomas’ doubts, (4) the coming of the Holy Spirit in Acts 2 occurred on Pentecost—a Sunday (some of the early church fathers suggested that His ascension to heaven also occurred on a Sunday). Initially the early church appears to have done “double-duty”—celebrating the traditional Sabbath on Saturdays in the synagogues or in the Temple in Jerusalem; after all, they still saw themselves as Jews. But for the particularly distinctive celebrations of their faith—the Lord’s Supper as well as the worship of Jesus as Lord—those they reserved as separate events commemorated on Sundays. Their Sundays would have also included study of the scriptures, prayer and possibly love feast meals where they all were joined together in Christian fellowship.
Now—other parts of the question. Daniel 7:25 is actually talking about the impact of the antichrist in the end times so that specific instance is probably not a part of this discussion. However, did a Roman emperor have any place in this move from Saturday to Sunday? No. It is suggested that the Roman emperor Constantine may have become a Christian. While we can’t be sure that he did that, we do know that he did enact the first civil law regarding Sundays in 321 AD, saying this: “On the venerable day of the sun let the magistrate and people residing in cities rest, and let all workshops be closed. In the country however, persons engaged in agricultural work may freely and lawfully continue their pursuits; because it often happens that another day is not so suitable for grain growing or for vine planting; lest by neglecting the proper moment for such operations the bounty of heaven should be lost.” Note his reference to the “day of the sun”; Constantine was a sun-worshiper before supposedly converting to Christianity. The fact is, since apostolic times, Sundays (for all the above reasons) had become a day of worship, meditation, and rest. As biblical scholar Gleason Archer says, “As the Lord’s Supper replaced the Old Testament sacrament of the Passover, as the death of Christ replaced the sacrifice of animal offerings on the altar, as the high priesthood of Christ replaced the priesthood of Aaron, and constituted every born-again believer as a priest of God, so also in the case of this one commandment out of the ten, which was in part at least ceremonial, there was to be a change in the symbol appropriate to the new dispensation” (Encyclopedia of Bible Difficulties, page 117). As to why it appears we don’t observe the Sabbath anymore, certainly some of it is our being impacted by the secular society in which we live, where Sunday appears no different than any other day of the week in terms of businesses open and people working. However, oddly enough, some people have actually blamed the apostle Paul, specifically regarding a verse he wrote to the Colossian church: Therefore do not let anyone judge you by what you eat or drink, or with regard to a religious festival, a New Moon celebration, or a Sabbath day—Paul, Colossians 2:16. Actually, in the Greek, a better translation would be “Sabbaths” (plural versus singular). Why is that important? Well, the Hebrew calendar not only marked regular weekly Sabbaths but also feast-day Sabbaths, regardless of when that day actually occurred in the week. What Paul is actually doing is not saying the Sabbath of the fourth commandment is no longer binding, but rather telling his readers that the old “holy days” of the Old Testament are no longer binding in the same way that the Passover and animal sacrifices are no longer binding due to the far greater excellence of the “once for all” sacrifice that Christ performed. In fact, immediately following that verse, he says, These are a shadow of the things that were to come; the reality, however, is found in Christ—Paul, Colossians 2:17. So how should we continue to obey and honor the Sabbath? Ironically, maybe an Old Testament passage can give us some insight: If you keep your feet from breaking the Sabbath and from doing as you please on my holy day, if you call the Sabbath a delight and the Lord’s holy day honorable, and if you honor it by not going your own way and not doing as you please or speaking idle words, then you will find your joy in the Lord, and I will cause you to ride in triumph on the heights of the land and to feast on the inheritance of your father Jacob”—God speaking, Isaiah 58:13-14. Is the Sabbath still God’s intention for us? Absolutely. Will its observance delight Him? Without question. And, as Peter and the disciples declared unequivocally to the Jewish religious leadership, We must obey God rather than men!—Acts 5:29. Remembering the Sabbath by keeping it holy, keeping it unlike any other day of the week, is still a command to be followed and obeyed. That will never change.