Should I ask a journal for provided peer review when a corresponding author will not share communications?
No, it's not appropriate. The whole peer-review system relies on the corresponding author's trustworthiness. Asking the journal to provide reviews to other authors is an implicit allegation that the corresponding author is not fulfilling their duties or possibly even engaged in misconduct. Unless there is actual misconduct involved or the corresponding author no longer available (e.g., sick) other authors should never contact the journal. Bringing this lack of communication among authors to the journal's attention is the last resort and will not only cost you a collaboration (and thereby make an enemy) but probably also prevent the publication. 

It even would be more appropriate to contact the corresponding author's superiors, although that would be a nuclear option too.

I would have a frank discussion with the corresponding author. I might even say that this could be the last collaboration if they don't start taking me serious.