Matthew 10:5 is the great commission. Matthew 10:6 tells them where to go. Rome was a Gentile city. The twelve were instructed by our Saviour Not to go there. Paul was later appointed Apostle to the Gentiles and He also was allowed to preach to the Israelites.
This is why you never see any scripture about Peter being in Rome. Paul established the Church in Rome and none of the twelve are ever shown to be there.
You are right on.