First, you say Peter made a mistake. Then when I call you out on that illogical statement, you go with the old restructuring of the sentence argument, saying that he was misunderstood. Apparently 3,000 + people misunderstood the Holy Spirit speaking through Peter on that day since they were baptized. And the Bible clearly says that those who were baptized that day were added to the church. In other words, they were saved. Just face the fact that you don't have a real answer for this verse.
The idea that repentance is tied to the remission of sins, and baptism is not, is a bogus one. The "and" in that passage between "Repent" and "be baptized", which as you must know is a conjunction, ties them together. The conjunction "and" never separates two things, always joins them. The Greek word here is "kai" and it has the meaning I just described. Even if you wanted to tie only one of the verbs to remission of sins, it would be baptism the way the sentence is structured. However, that is not the case since the Bible clearly teaches that repentance is necessary for salvation.
If this is a scriptural teaching , please post all the scripture here so we can see it