Peter wasn't told to do it, Paul was chosen Acts 9:11-16. Peter never set foot in Rome in the scriptures and everything you read about him indicates he was far from there.
The scripture you quote is the last time we hear of Peter in the book of Acts and everything about him thereafter in the scriptures point to him being in Babylon and that's exactly where many of the "Lost Sheep" were. This is about the fourteenth paragraph down...."At the beginning of the present era there were many conversions to Judaism all over the Middle East. In about 40 CE, in northern Iraq, the Royal Family and many of the people of Adiabene became Jews. It is estimated that there may have been as many as one million Jews around Babylonia at that time."
Yes, Paul was chosen, which nobody denies. But Peter was also told by God, no less, that the Gentiles should hear the gospel by his very mouth. Do you deny scripture:
The key phrase here is in the scriptures. Where does scripture indicate that every single action of the Apostles was recorded? The scriptures don't say one way or the other whether Peter was ever in Rome. So to find out we must rely sources outside scripture.