the Delta Quadrant, and there that's when they tell the crew about the “real” mission. The crew ...
The crew would just return the ship to base.
the former commodore and his friends force them to obey
Force how? Continuously at gun point? Do the JemHadar thing and poison the Starfleet personnel and only provide the antidotes if they preform?
The crew is going to know about the demotion and the brig time, prior to boarding the ship. Using the modern US Navy for example, the bulk of the crew, and certainly the chiefs, know who a ship's commanding officer is going to be usually before that officer is told. When a new commandig officer boards their vessel for the first time, everyone knows them, so they can address them correctly.
Your Captain and his special friends is going to end up locked in their quarters with the computers disconnected.