One possible reason that Paul and Peter did not include more gospleGospel details in their letters is that they were apostolically responsible for overseeing the creation of two of the Gospels. Thus they could always point their disciples to those Gospels for study and meditation.
Peter and John Mark (author of Mark) were close friends, as shown in Acts. Many scholars believe that Peter was the priomary source for Mark's gospel.
Paul and Luke (author of Luke) traveled together on some of Paul's missionary journeys. When Paul speaks in Romans 2:16 about "my gospel", some scholars think that Paul is referring to the Gospel of Luke. Luke also made contact with Mark, so got some of his material from him.
Some of these connections are explored in this article: