I am a 3rd-timer postdoc, and I often run into this issue. Over my career I have greatly benefitted personally of responsible peer review and participating in the elaboration of 'Response to Reviews'. Moreover I am very wary of publishing ethics, and open discussion of papers after publication.
This is often what happens: the 1st author of a paper where I am a co-author assigns a PI as last corresponding author. This PI is usually older and actually less invested in the project, but wishes to handle the submission. This person will however not share any correspondence with editors or submission files with authors other than the first (and I suspect even then not in full). I am thus left in the dark about discussions over papers where quite often I made a major part of the writing and experiments, and the only specialist about core topics being discussed.
I have tried asking for the details of peer review and was ignored, every time this happened. On a most recent case I received editorial notification of submission of same paper from two different journals within the time span of just 5 days, and now I fear somebody pulled a duplicate submission! This kind of attitude has made me reluctant of handing the position as corresponding authors to others, particularly to PIs, which is politically not good.
Thus I ask: How do others deal with such a situation?
UPDATE 1 (24.01.2018): I have just sent an email to the PI politely asking again for the peer reviews stating I will follow up with the journals if there is no reply.
UPDATE 2 (25.01.2018): First author responded informally providing the dates of all submission and general reasons for two rejections. The details didn't really add up, but given a casual tone perhaps it wasn't precise (e.g. I suspect this person is not aware of the difference of editor x reviewer). I still asked again for the Reviewers reports, and was left with the impression the 1st author did not (care to) see them either. She said she'll ask the PI.
In case I get no response I am not sure on how to proceed (e.g. if I want to see peer review from a previous journal).