Yes, Peter was in Rome -- you have a number of his contempories, near-contempories and Church fathers who wrote so:
Tertullian,
in The Demurrer Against the Heretics (A.D. 200), noted of Rome, “How happy is that church . . . where Peter endured a passion like that of the Lord, where Paul was crowned in a death like John’s [referring to John the Baptist, both he and Paul being beheaded].” Fundamentalists admit Paul died in Rome, so the implication from Tertullian is that Peter also must have been there. It was commonly accepted, from the very first, that both Peter and Paul were martyred at Rome, probably in the Neronian persecution in the 60s.
In the same book, Tertullian wrote that “this is the way in which the apostolic churches transmit their lists: like the church of the Smyrnaeans, which records that Polycarp was placed there by John; like the church of the Romans, where Clement was ordained by Peter.” This Clement, known as Clement of Rome, later would be the fourth pope. (Note that Tertullian didn’t say Peter consecrated Clement as pope, which would have been impossible since a pope doesn’t consecrate his own successor; he merely ordained Clement as priest.) Clement wrote his
Letter to the Corinthians perhaps before the year 70, just a few years after Peter and Paul were killed; in it he made reference to Peter ending his life where Paul ended his.
In his
Letter to the Romans (A.D. 110), Ignatius of Antioch remarked that he could not command the Roman Christians the way Peter and Paul once did, such a comment making sense only if Peter had been a leader, if not the leader, of the church in Rome.
Irenaeus, in
Against Heresies (A.D. 190), said that Matthew wrote his Gospel “while Peter and Paul were evangelizing in Rome and laying the foundation of the Church.” A few lines later he notes that Linus was named as Peter’s successor, that is, the second pope, and that next in line were Anacletus (also known as Cletus), and then Clement of Rome.
Clement of Alexandria wrote at the turn of the third century. A fragment of his work
Sketches is preserved in Eusebius of Caesarea’s
Ecclesiastical History, the first history of the Church. Clement wrote, “When Peter preached the word publicly at Rome, and declared the gospel by the Spirit, many who were present requested that Mark, who had been for a long time his follower and who remembered his sayings, should write down what had been proclaimed.”
Lactantius, in a treatise called
The Death of the Persecutors, written around 318, noted that “When Nero was already reigning (Nero reigned from 54–68), Peter came to Rome, where, in virtue of the performance of certain miracles which he worked by that power of God which had been given to him, he converted many to righteousness and established a firm and steadfast temple to God.”
These citations could be multiplied. (Refer to Jurgens’ books or to the Catholic Answers tract
Peter’s Roman Residency.) No ancient writer claimed Peter ended his life anywhere other than in Rome. On the question of Peter’s whereabouts they are in agreement, and their cumulative testimony carries enormous weight.
Typical Religion of man.
Throw away the perfect Words of God for the imperfect histories of man.
Our final authority is the Bible itself - the Words of God.
Not man’s histories.
Peter was among three who struck hands with Paul and Barnabas (Galatians 2:7-9) that Peter, James and John would go to the circumcision (Jews) and Paul and Barnabas would go to the uncircumcision (Gentiles). They even had separate gospels (that is the news preached to the the two groupings of people had some different elements with regard to their responsibility to God through the period of the Acts.)
Peter was not a minister to the Gentiles, with the exception of one household at Caesarea (Acts 10), prior to the agreement recorded in Galatians ch. 2 (corresponding with Acts 15) while still preaching the imminent return of Christ as King, upon the condition of Israel’s repentance.
Since the Bible trumps the histories of man, we may easily conclude that the documents you cite underwent some serious tampering through the years in favor of your religious system. Romish religious leaders have been known to do that, as well as tamper with the Bible itself in favor of Romish theologies.
Paul’s words (Roams through Philemon) would easily trump those of Tertullian. And Peter never mentions Rome in his epistles.
But, Tertullian is an interesting fellow, and we’ve read enough about him to know that he certainly would not have been in agreement with the apostate sacraments and teachings of the WCC (RCC). And so, I would sooner believe that someone tampered with Tertullian’s writings, or created entirely fraudulent documents and attached his name.