We don't have a record of what Peter taught when he was mistaken, but we know he was for a while. He had to be corrected 3 times; by Paul, by the sheet vision and by the tongues episode when the non-Jewish people believed.
I realize that this will fall on deaf ears where you are concerned, but perhaps someone else will receive it with ears to hear...
In Matthew 12:30-32, The warned Israel that they would be forgiven for going against the Father, and forgiven for going against the Son, but not for going against, or resisting the Spirit.
Why the one and not the other two also?
In Mark 7:27the Lord told the Syrophenician who came seeking a blessing "Let the children
first be filled:"
In Acts 3, the Spirit through Peter, reminded Israel:
25. Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.
26. Unto you
first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.
Inn Acts 7:51, the Spirit through Stephan "Ye stiffnecked and uncircumcised in heart and ears,
ye do always resist the Holy Ghost: as your fathers did,
so do ye."
In Acts 13: 46, we read "Then Paul and Barnabas waxed bold, and said, It was necessary that the word of God should first have been spoken to you: but seeing ye put it from you, and judge yourselves unworthy of everlasting life, lo, we turn to the Gentiles."
The same is related by Paul in Acts 18:6, and one final time in Acts 26: 28.
In Acts 10, Peter was not being corrected, rather; he was being prepared for a change, as Israel had already been judged as unfit for their missionary role by the Spirit as they had having resisted the Spirit.
Their reply? Murdering Stephan; who then saw the Lord standing - a sign of judgment, Isaiah 3:13, for example.
Later, in Acts 15, Peter will be able to assert the following, in support of Paul's ministry among the Gentiles without their need to submit to circumcision and the Law:
7. And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe.
8. And God, which knoweth the hearts, bare them witness, giving them the Holy Ghost, even as he did unto us;
9. And put no difference between us and them, purifying their hearts by faith.
James adds to that, in that same chapter:
14. Simeon hath declared how God at the first did visit the Gentiles, to take out of them a people for his name.
15. And to this agree the words of the prophets; as it is written,
16. After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up:
17. That the residue of men might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things.
18. Known unto God are all his works from the beginning of the world.
19. Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
20. But that we write unto them, that they abstain from pollutions of idols, and from fornication, and from things strangled, and from blood.
Study out Matthew 10 in its entirety, and what you find is that when He sent them "to the lost sheep of the house of Israel," He then prophesied in that very same chapter of Matthew, what would happen to them as to that in Early Acts.
The order was the lost sheep of the house of Israel first, then His other sheep not of that fold - Judaea and Samaria [the balance of Israel's 12 Tribes], and then through them; the uttermost parts of the earth, Acts 1:8.
And all that hinged on this here - Matthew 10:
19. But when they deliver you up, take no thought how or what ye shall speak: for it shall be given you in that same hour what ye shall speak.
20. For it is not ye that speak, but the Spirit of your Father which speaketh in you.
21. And the brother shall deliver up the brother to death, and the father the child: and the children shall rise up against their parents, and cause them to be put to death.
22. And ye shall be hated of all men for my name's sake: but he that endureth to the end shall be saved.
23.
But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come.[/B]
And that is this here - Matthew 24:
9. Then shall they deliver you up to be afflicted, and shall kill you: and ye shall be hated of all nations for my name's sake.
10. And then shall many be offended, and shall betray one another, and shall hate one another.
11. And many false prophets shall rise, and shall deceive many.
12. And because iniquity shall abound, the love of many shall wax cold.
13. But he that shall endure unto the end, the same shall be saved.
14. And this gospel of the kingdom shall be preached in all the world for a witness unto all nations; and then shall the end come.
And that is tied to this, from this same Matthew 24 chapter:
34. Verily I say unto you, This generation shall not pass, till all these things be fulfilled.
35. Heaven and earth shall pass away, but my words shall not pass away.
36. But of that day and hour knoweth no man, no, not the angels of heaven, but my Father only.
37. But as the days of Noe were, so shall also the coming of the Son of man be.
In short, Peter and his fellow Apostles had their commission temporarily interrupted to another day.
But of course, that does not fit your 70AD errors, so it must be that Peter was the one needing the correcting, not you in your resistance of this truth.