Couldn't all of this been avoided if Jellico had taken Riiker aside and told:
1. Picard's mission makes him expendable.
2. We may be on the brink of war.
3. Because we may be going to war, I need you to make sure that my orders are followed without question.
4. If you can't do that I'll reassign you.
5. You are ordered to not discuss this with anyone.
I feel like all of those points go without saying though wouldn't they. Most of them seem like they should be a given except for number 5.
Regarding Jellico ignoring his staff I don't think thats the case either. Just because he didn't go with their suggestions didn't mean that he did not listen to them. There was no justification for Riker's behavior. Again, if we are comparing egos here Jellico asked Riker to fly a the shuttle in support of the mission even when Riker made him ask him to.