Just short of any unwavering respect wouldn't fly with Jellico.
And you're assuming she'd ever show any disrespect to a
direct superior. Anything even resembling that which she is guilty of only happens with one officer who is not her direct superior. Outside of that, she has all of command backing her up, suggesting that she is indeed capable of being a reliable subordinate
JELLICO: Did you beam down to the planet an hour earlier than I ordered?
SHELBY: Yes, sir. I wasn't aware you wanted to be informed.
JELLICO: I can see why you're still only a first officer. I expect to be notified if there's been a change to my orders.
SHELBY: Really, Captain, if we ran into the Borg here, two extra bodies wouldn't've made a hell of a difference, now would they? We had three hours before the storm front hit, less than two hours now. Data was available. I took him. We came. I don't see your problem.
JELLICO: Are you questioning my judgment, commander?
SHELBY: Do I need to remind you that I am here on the authority of admiral --
JELLICO: You're relieved. Don't make me confine you to quarters as well.
That's a very slanted take on both her & him imho. This whole point hinges on saying she
would beam down without her direct superior officer knowing about it, the captain, & person in command of the mission. Riker is none of those things. He's just an officer involved that outranks her. You're skipping over the part where she was brought there to not only replace him, but to in fact take action on the mission for high command. It's a specialist mission, not a permanent assignment. Not yet anyhow
After their conversation in his quarters it's mostly clear that he's staying so it's a stretch that there's confusion.
There's confusion about who she answers to. Just because he's the 1st officer doesn't necessarily mean she is required to answer to him, & if she is, then she's learning that on the fly, & yet still being asked to proceed with what she was brought there to do, by people higher up than him. He is in the way of that
Or maybe she's not right? Maybe it would be a bad call to use the saucer separation that soon in the battle. Presumably Riker has more experience with it than she does and infinitely more experience with how the crew would have handled it. Ultimately they use the separation as Picard had decided as a backup plan.
Maybe maybe maybe. Her suggestions don't just come out of nowhere. She's been making them for months back at command. So... (Maybe game) Maybe Picard doesn't decide to use her plan as a backup, if he never finds out about it in the manner she wants it represented. Enough maybes. What we know is that she was brought in for suggestions just like that one. Ones that admirals want to hear. So probably ones that captains want to hear too, & ones that 1st officers might need to agree to first, but.... she didn't seem to know that, as I said above
They didn't like each other at that point but BoBW proves Riker finds a way to work with those he doesn't like or get along with. But Jellico gave up on Picard, that's their main disagreement in that scene... it's totally a misrepresentation of the episode to make it seem like anything else
Once again, forgetting that his plan
saved Picard's life, precisely because it gave them the advantage. Without having the advantage on them, you don't, unless you start lining up warships, & probably not even then. Certainly not if you fly off on a half-cocked rescue op, that they are certainly expecting. It's only giving up on Picard in that it's admitting that they are in no position to prioritize him above other concerns, least of all, when they don't even really know if the guy is even still alive.
The answer to Riker's question of "Shouldn't we assume he is alive until we know otherwise?" is "Under the circumstances? Hell no. We assume he's dead, because he probably should be." We assume he's caught as a spy. We know there was a firefight. So, now he's also a terrorist. We assume he's tortured for information that they'll probably get, & do, & then when they have no further use of him, we assume they exact retribution by murdering him, at some unknown location. We assume they're lying to us about returning him, if we cave in & give back worlds, worlds they're already mounting an invasion on. We assume nothing that guy said is true, & we act on what we know we can, & not on what they tell us we can.
Remember when Data brought Worf up on insubordination and spoke to him privately, it took like 5 minutes and they still remained friends. Jellico with some strategic diplomacy with Riker could have achieved the same thing here
Even though he wasn't going to do what Riker demanded he do, louder than I'd ever heard him yell at anyone? The man is not talking Riker down from the fact that the primary goal is NOT going after Picard, nor admitting the entire Federation's complicity. That is what Riker wants, & it's not happening. So the only way Riker's behavior gets verbally deescalated is if Jellico caves & just does what he wants. Need I remind you who's in charge here?
That's also not the same as Worf's minor verbalization of disgruntlement at all. It is literally Riker openly & defiantly challenging the man's command, & that is why Troi is trying to stop him before it goes there, because as an empath, she already knows that Riker isn't winning this one, & if he wants any hope of getting a chance to have anything the way he'd want it, he ought to shut up
But he won't, because he is emotionally compromised, as he ALWAYS is when Picard's life is in jeopardy, & not only is he not thinking clearly, he is suggesting one of the dumbest ideas in all of brinkmanship... not just trading entire star systems for one man's life, but potentially reigniting the spark of war between 2 superpowers over a man's life, who he only
thinks might be alive, because that other superpower lorded that possibility over him, like a carrot in front of a donkey. He's the suckiest sucker that ever sucked imho
Everything goes swimmingly when they come up with a risky attack / rescue plan which is kind of what Riker was asking for earlier in the episode.
It's absolutely nothing like what Riker was suggesting. He demanded they publicly implicate all of Starfleet in Picard's mission, so he could have the protection of a POW, which, newsflash, means you all were acting as the enemy, like you used to be, before all that peace treaty/armistice stuff, & thereby, YOU are now the military aggressor. Maybe you get your ass handed to you at the diplomacy table over that, & lose whole worlds because of it, OR maybe you end up getting billions of people killed because of it. The only way you know which they intend to do is by trusting what the duplicitous negotiator is telling you
Nechayev never says they won't go to war. She says she hopes they won't have to. That means it's a very real possibility. Admitting Starfleet's complicity jeopardizes everyone. The other part of Riker's brilliantly thought out plan is charging out to rescue the guy, which they'll undoubtedly be squeeing like schoolgirls over the hope that you will, as it just makes it even more obvious that you are the aggressors. It undermines everything the Federation is supposed to stand for. It could crumble all the support the UFP has as being a passive conglomerate. "We got Picard" is the bait. Are you really going to be dumb enough to just bite that right off?
However... Jellico's plan is to investigate. Find out a way to get ahead of this ball. Determine what they are up to, so they can craft a method for how to intervene intelligently, by doing the
right thing, instead of just "DO SOMETHING", which is basically all Riker is offering. Jellico's plan is to
stop them, get them on the defensive, take back the advantage, & because he's thinking clearly like that, & he knows how to aim a very excellent crew, he's able to find what he needs, & use it to get exactly where he needs to be
Besides, if we're debating over which plan is the one everyone should be getting behind... need I remind you who is in charge?