Do you know what I'd do under these circumstances - a rhetorical question.
I would start a database logging just who did the pressuring. Most of the crew of that airline would have to agree. It would be database held privately, but all relevant flight details recorded. Possibly, a copy of the plog and fuel receipts.
Boxes to tick. Is the bloke qualified? In addition to this, do they, or did they, hold ALTP / ATPL / ATP, and were they ever fully operational aircrew?
I would guess there are not may people that can tell the skipper what to do and it would be interesting to see any spikes in a graph pointing towards individuals who are company-minded to the point of obsession.
Before you go into hyper-spuffle, I can tell you, I've met a few of these.