1. Then it would be just as possible for the descendants of the ten tribes, who lost their identity, and were thoroughly sifted among the nations [goyim-gentiles] (Amo 9:9) to have been in the same area , right?
2. It is evidently not meant here that Paul was to preach only to the gentiles and Peter only to the Jews , for Paul often preached in synagogues with both Jews and gentiles, and Peter was the first who preached to a "gentile" (Acts 10); but it is meant that it was the main business of Paul to preach to the gentiles, or that this was especially entrusted to him.
3. Paul and Peter preaching in different regions of Galatia is a moot point in our context. Peter makes a reference to Hos 1:10:2:23 in referring to his audience as those “
who once were not a people but are now the people of God” and shared the same status as their forefathers who were deemed a chosen generation, royal priesthood, and holy nation (Ex 19:6;1 Pet 2:9-10). Paul refers to the same Hosean scriptures in Rom 9:25-26 directing it to his audience of “gentiles” living in Rome.
Hosea was a prophet sent to the Northern 10 tribes (Hos 1:4,6) who, in the 1st century, were dispersed in Galatia and other parts of the Empire, living as "strangers". These are the "gentiles" Peter and Paul are addressing, fulfilling the New Covenant promise (Jer 31:31-33) to the house of Israel--the ten Northern tribes! Notice the status once held by these dispersed pilgrims/strangers in Asia Minor you claim are Jews:
1 Pet 4:3 It is quite enough to have done as pagans choose to do, during the time gone by! You used to lead lives of sensuality, lust, carousing, revelry, dissipation and illicit idolatry, (Moffatt)
It is highly unlikely the Jewish congregants would have once led a life of sensuality, lust, carousing, revelry, dissipation, and idolatry without being killed (remember Stephen?).
But the Greek-speaking, dispersed, house of Israel, who lost their status as God's people, and were promised redemption in the state and place where we find them in the 1st century (Hos 1:10), would have. As prophesied by Hosea and confirmed by Peter, and Paul:
Hos 1:10 "Yet the number of the children of Israel Shall be as the sand of the sea, Which cannot be measured or numbered. And it shall come to pass In the place where it was said to them, 'You are not My people,' There it shall be said to them, 'You are sons of the living God
Hos 2:23 Then I will sow her [house of Israel] for Myself in the earth, And I will have mercy on her who had not obtained mercy; Then I will say to those who were not My people, 'You are My people!' And they shall say, 'You are my God!' "
1Pe 2:10 who once were not a people but are now the people of God, who had not obtained mercy but now have obtained mercy.
Rom 9:25-26 As He says also in Hosea: "I WILL CALL THEM MY PEOPLE, WHO WERE NOT MY PEOPLE, AND HER BELOVED, WHO WAS NOT BELOVED." 26 "AND IT SHALL COME TO PASS IN THE PLACE WHERE IT WAS SAID TO THEM, 'YOU ARE NOT MY PEOPLE,' THERE THEY SHALL BE CALLED SONS OF THE LIVING GOD."
Notice Hosea 1:10 states they cannot be measured or numbered. That's true in quantity as well as quality. If they cannot be identified (quality), then it stands to reason they cannot be numbered. For me, there's only one conclusion and it all lines up with scripture. The gentiles to whom the apostles were sent were the lost descendants of Jacob, who by then were a mixed multitude living as gentile Romans, Greeks, etc., unawares of their ancestral identity, just as I was, and perhaps you and others on this forum who love the LORD.