The first notion to dispel is, that scripture identifies there being only one church in existence.
There was a church ( a congregation) in the wilderness before Christ came that worshiped the Lord...........[Acts 7:38 KJV] 38 This is he, that was in the church in the wilderness with the angel which spake to him in the mount Sina, and [with] our fathers: who received the lively oracles to give unto us:
[Exodus 34:14 KJV] 14 For thou shalt worship no other god: for the LORD, whose name [is] Jealous, [is] a jealous God:
If this church is acknowledged, is it unimaginable that there could be others formed during other dispensations?
Moses and the Israelites wandering in the wilderness was not the Christian Church that Jesus built, built on the foundation that he was the Messiah and the Son of God (Matthew 16:16-18).
......The Lord ADDED to them, the existing church, the church Jesus built during his time on earth. A new church was NOT formed at Pentecost. This church continued thru, and beyond the conversion of Paul.
Correct. Jesus commanded them to increase the membership of the Church - Matthew 28:19-20 (WEB):
(19) Go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
(20) teaching them to observe all things that I commanded you. Behold, I am with you always, even to the end of the age.” Amen.
Paul was saved and chosen by the Lord Jesus to be an apostle to the Gentiles...........[Romans 11:13 KJV] 13 For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
Peter and Paul had separate apostleship..............[Galatians 2:8 KJV] 8 (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)..........Peter was apostle to the Jews, and Paul to the Gentiles.
As Fred J has just pointed out, Paul was called to be an apostle to both the Gentiles and the Jews - Acts 9:15 (WEB):
(15) But the Lord said to him, “Go your way, for he is my chosen vessel to bear my name before the nations and kings, and the children of Israel.
As Barnes' Notes says:
And the children of Israel - The Jews. This was done. He immediately began to preach to them, Act_9:20-22. Wherever he went, he preached the gospel first to them, and then to the Gentiles, Act_13:46; Act_28:17.
Peter and Paul were not apostles over the same church. Their was no animosity between Peter and Paul. Paul could never have been selected as an apostle to the church in Jerusalem because he didn't meet the requirements.
Again there is just one Church, the one which Jesus established and has been growing in numbers since that time (and which Paul referred to as the church of God). Paul was not an apostle "to the church" in any place, he was an apostle of Jesus for all Christians in all places - 1 Corinthians 1:1-2 (WEB):
(1) Paul, called to be an apostle of Jesus Christ through the will of God, and our brother Sosthenes,
(2) to the assembly of God which is at Corinth; those who are sanctified in Christ Jesus, called saints, with all who call on the name of our Lord Jesus Christ in every place, both theirs and ours:
There is just one bride of Christ, the Church, not multiple brides. There is just one body of Christ, the Church (Colossians 1:18,24), not multiple bodies - 1 Corinthians 12:12-14 (WEB):
(12) For as the body is one, and has many members, and all the members of the body, being many, are one body; so also is Christ.
(13) For in one Spirit we were all baptized into one body, whether Jews or Greeks, whether bond or free; and were all given to drink into one Spirit.
(14) For the body is not one member, but many.
Colossians 1:18 ISV
(18) He is also the head of the body, which is the church. ...
Nowhere was the church in Jerusalem, overseen by Peter and the apostles, referred to as being the body of Christ.
No specific congregation is referred to as the body of Christ. Here are the only four verses that use the phrase "body of Christ":
Romans 7:4 WEB
(4) Therefore, my brothers, you also were made dead to the law through the body of Christ, that you would be joined to another, to him who was raised from the dead, that we might produce fruit to God.
1 Corinthians 10:16 WEB
(16) The cup of blessing which we bless, isn’t it a sharing of the blood of Christ? The bread which we break, isn’t it a sharing of the body of Christ?
1 Corinthians 12:27 WEB
(27) Now you are the body of Christ, and members individually.
Ephesians 4:12 WEB
(12) for the perfecting of the saints, to the work of serving, to the building up of the body of Christ;
Nowhere was it said that Jew and Gentile were one body in the church overseen by Peter.
Peter also preached to Gentiles. Peter considered Paul to be a member of the same Church and agreed with all of Paul's letters - 2 Peter 3:15-16 WEB
(15) Regard the patience of our Lord as salvation; even as our beloved brother Paul also, according to the wisdom given to him, wrote to you;
(16) as also in all of his letters, speaking in them of these things. In those, there are some things that are hard to understand, which the ignorant and unsettled twist, as they also do to the other Scriptures, to their own destruction.
Paul said that the body of Christ would sit in heavenly places..........[Ephesians 1:3 KJV] 3 Blessed [be] the God and Father of our Lord Jesus Christ, who hath blessed us with all spiritual blessings in heavenly [places] in Christ:
That passage doesn't mention the body of Christ. Are you suggesting that only the Ephesians were member of the body of Christ?! The word "us" is referring to all Christians.
.....Only Israel was told they would be a kingdom of priests. Nowhere does Paul say the members of the body of Christ are, or will be made priests; this differentiates Peter's church from the body of Christ. Only Peter's church could have the expectation of being priests in the kingdom on earth.
Exodus 19:5-6 WEB
(5) Now therefore, if you will indeed obey my voice, and keep my covenant, then you shall be my own possession from among all peoples; for all the earth is mine;
(6) and you shall be to me a kingdom of priests, and a holy nation.’ These are the words which you shall speak to the children of Israel.”
Sadly the Israelites did not obey and keep the covenant, so they did not become a kingdom of priests.
1 Peter 2:9-10 WEB
(9) But you are a chosen race, a royal priesthood, a holy nation, a people for God’s own possession, that you may proclaim the excellence of him who called you out of darkness into his marvelous light:
(10) who in time past were no people, but now are God’s people, who had not obtained mercy, but now have obtained mercy.
Peter is talking about Gentiles ("who in time past were no people") now becoming God's people. He is not referring to the "believing remnant of Israel", yet you claim that Peter was "apostle to the Jews".
The body of Christ is not the same church as Peter's church. Neither is it Peter's church fully manifested in knowledge thru the completed progressive revelation given to the apostle Paul. These two churches have different apostles. These two churches have different destinies; Peter's church is destined to reign with Christ on earth; the body of Christ is destined to dwell in heavenly places. Two churches with different purposes; Peter's church will reconcile the earth and be a blessing to the nations in the kingdom on earth; the body of Christ will reconcile the heavens and make know the wisdom of God. Scripture presents two distinct churches in Christ Jesus.
Revelation 20:6 WEB
(6) Blessed and holy is he who has part in the first resurrection. Over these, the second death has no power, but they will be priests of God and of Christ, and will reign with him one thousand years.
All Christians will have a part in the first resurrection, and all will reign with Christ. There is no splitting into reigning over earth and heaven. Christians are destined to judge both humans and angels, not one or the other - 1 Corinthians 6:2-3 (WEB):
(2) Don’t you know that the saints will judge the world? And if the world is judged by you, are you unworthy to judge the smallest matters?
(3) Don’t you know that we will judge angels? How much more, things that pertain to this life?