There are indications of interaction between the apostles Paul and Peter, and their churches.
Both apostles refer to each other in their letters. They assumed that their readers were aware of the other apostles. In a context of Christian unity, Paul mentions Cephas (Peter) in 1 Cor 1.11. Similarly, Peter mentions Paul’s epistles in the same breath as ‘the other Scriptures.’ Neither criticises the other.
There is a different situation in Gal 2, where Paul does refer critically to Peter, although only in respect of a specific incident. Paul does not criticise his ministry. In fact in the first part of that chapter, Paul indicates agreement with Peter and the other apostles in Jerusalem.
Silas and Mark both worked with Paul and Peter at different times.
Some churches were in relationship with different apostles at different times. For example, Ephesus and Laodicea are both referred to in relation to Paul and John. Churches in Galatia are both addressed by Paul and Peter. The reasons for these changes are not given. From other scriptures we assume teamwork and unity, not division.
The New Testament does not lay down a strict formula for the way apostles interacted, or how workers or churches moved between them. Such a formulaic approach is out of keeping with the ‘way of life’ presented in the NT.
Similarly, the values of the NT include unity, teamwork, support, friendship, co-operation. Where, for example, workers serve with both Paul and Peter, we would want to draw the conclusion that they did so with full agreement and commendation. The alternative, of frequent fallings out, cannot be commended.