Yes the signs and wonders were to convince the Jews that Paul was a legitimate apostle, equal to the other 12, and his new gospel of grace was similarly authenticated by God. Recall Acts 15:12
12 Then all the multitude kept silence, and gave audience to Barnabas and Paul, declaring what miracles and wonders God had wrought among the Gentiles by them.
Signs and wonders were critical in the decision at the end of Acts 15, that the gospel of the uncircumcision, preached to the gentiles, was as legitimate as the gospel of the circumcision.
If Peter preached the Gospel to the Jews and Paul preached it to the Gentiles, that doesn't mean there were two gospels.
You should read the opening of the epistle to see what Paul thinks about other gospels.
Galatians 1
6 I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel:
7 Which is not another; but there be some that trouble you, and would pervert the gospel of Christ.
8
But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed.
9 As we said before, so say I now again,
if any man preach any other gospel unto you than that ye have received, let him be accursed.
Paul wasn't saying Peter was preaching another Gospel and then cursing him. And Peter pointed out in Acts 15:7, "God made choice among us, that the Gentiles by my mouth should hear the word of the
gospel, and believe.". And in Acts 9, we read that Ananias heard the Lord speak the following about Paul's calling. "15 But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the
Gentiles, and kings, and the children of
Israel: " Their calling wasn't exclusive and their gospels were not different or contradictory.
See also his comments in Romans 10.
8 But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is,
the word of faith, which we preach;
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
11 For the scripture saith, Whosoever believeth on him shall not be ashamed.
12 For
there is no difference between the Jew and the Greek: for the same Lord over all is rich unto all that call upon him.
and he calls their preaching 'gospel' in this chapter.
15 And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach
the gospel of peace, and bring glad tidings of good things!
You really have to repent and prioritize the word of God over the dispensationalism. The hyperdispensational stuff can be damaging. Look at the warning in Galatians 1. Do you really want to advocate for two gospels considering that?