Now, to answer your questions.
Are there on one peop[le of God, or two peoples of God, Israel and the Church?
Israel is the people of God, but they are not children of God. They occupy the OT and have a relationship with God. They are a nation of people and servants of God.
The church of Jesus Christ is not a subject of the OT prophets and is a mystery hidden in ages past and revealed as a new entity after the resurrection Jesus Christ. It is presented as a living organism, the body of Christ and the bride that is espoused to him and is foreshadowed in an absolutely marvelous way by the story of Adam and Eve, how Adam was put to sleep by God while he took his rib and fashioned Eve from his body and then presented her to him as his bride. This is what happened at the cross when "God has made him to be sin for us who knew no sin that we might be made the righteousness of God in him." The soldier pierced his side with the sword and blood and water came out. The pure blood of God came out which can cleanse us of our sins and the water came out, which is symbolic of the Spirit of God, who can give us eternal life by his eternal presence in us. The life of the flesh is in the blood and the Spirit is the life of God and Jesus shed both on the cross for us as he paid the ultimate price for our sins that day.
All people who permanently possess the Spirit of God in their bodies are sons of God. This is what it means to be born again.
was the church plan B, aftre thought in mind of God, or always his primary plan?
No, but the inclusion of the gentiles into this body was a contingency based on the unbelief of the nation of Israel.
Now, I would like to prove that to the person who believes the words of scripture.
Rom 11:13 For I speak to you Gentiles,
What I am getting ready to quote is directed at gentiles as opposed to Israel, according to the text I am quoting. I keep reminding you that Paul wrote this in 58 AD. The tenses of the verbs are very important when studying the scriptures. Time elements are very important. Events relative to the time is very important. The actual words and to whom they are directed are of utmost importance. See context.
In AD 30 Jesus Christ was crucified and was buried and rose from the dead.
40 days later he ascended from earth to heaven with a promise he would come back in like manner.
10 days later God sent the Holy Spirit from heaven upon Israel with the same properties in the spiritual as rain water from heaven is in the physical. No one can live without water and those who live must drink. The rain water falls all over the earth and it falls in such abundance that no one can commercialize and deny it from others and it is always available to be consumed. It rains on the just and the unjust. It is available to all.
Re 22:17 And the Spirit and the bride say, Come. And let him that heareth say, Come. And let him that is athirst come. And whosoever will, let him take the water of life freely.
Jn 7:37 In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink.
38 He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water.
39 (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified)
Now, here is the quote to the gentiles from Romans 11;
25 For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.
26 And so (and so means after the fullness of the gentiles be come in as demanded by the context) all Israel shall be saved (s opposed to a remnant of them as before): as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
27 For this is my covenant unto them, when I shall take away their sins.
28 As concerning the gospel, they are enemies for your sakes: but as touching the election, they are beloved for the father's sakes.
29 For the gifts and calling of God are without repentance.
30 For as ye in times past have not believed God, yet have now obtained mercy through their unbelief:
31 Even so have these also now not believed, that through your mercy they also may obtain mercy.
32 For God hath concluded them all in unbelief, that he might have mercy upon all.
There is safety in believing the words.