Actually Peter had been a part of the problem of being a Judaizer and had to be confronted by Paul for causing division in the church (read Gal 2:11)
Jesus said if a brother sins against you or in some versions it just says sins, that you are to go to him alone and tell him about it just between you and him, but in fact Paul told the whole world.
Well one thing I know is Rome is “babylon “ now>>>>>>
I believe it is the mother Church which are the Catholic Church and her daughters the Protestants.
Honestly I wish I did not believe some of the things I do and not really educated enough on it to know if I understand it correctly or not.
But on the other hand we might be better off ( at least speaking for myself if we knew nothing but the gospel of Jesus.
I shall call you brother or sister hereafter in my prayers when you come up! So well said ...