You definitely bring up an interesting point when you state their relationship like this. Most focus on how Vermouth feels about the Organization in general instead of how Vermouth feels about the boss and the consequences of that. I feel like it is the opposite conclusion, the boss values Vermouth, but does not care about her with the depth or strength she does for him. The boss seems to have some concrete reason for caring about Vermouth (like she doesn't age), but Vermouth seems to care about the boss deeply as a person rather than for a certain reason.
There must be something keeping Vermouth loyal to the boss. She still does follow his orders -- she genuinely seemed to care (and not be angry) when the boss pulled her leash short after the haunted ship disaster. Vermouth doesn't sabotage the Organization in all the ways she is capable of without being caught for some reason. However, whatever that loyalty tie is, it doesn't keep her from allowing people to undermine the boss's will - the his plans and Organization's operation. Vermouth appears to dislike whatever the goal of the Organization is as far as the Miyanos go and seems to care little for the success or failure of its other plans, like Kir's assassination plot (She almost saw it as a game - could Conan stop them in time?).
The only way I can get these two conflicted impressions to tie is if Vermouth values the boss as a person, but resents his aspirations and even the Organization itself. To put the point in the form of a story, maybe Vermouth was close to the boss before the Organization, but she did not support whatever his desire was that prompted the boss to form it. There was some reason (maybe Vermouth had a one-sided attraction towards the boss, both of them no longer aging, etc.) Vermouth felt she couldn't deny him when he wanted her to join him with his plans, but she never liked his plans to begin with and liked them less over time. The boss meanwhile, never saw how his dream was straining Vermouth internally; the boss is happy to keep using her even though he says she is close no matter how she feels.
I feel like this explains why she wants the Organization brought down, yet did not take the opportunity to sabotage it herself, or allow the FBI or the police or whoever else to do it for her. Instead Vermouth supports Conan, for whatever virtues she sees in him to do the job. "If he could reach my heart, maybe he could be our long awaited silver bullet..." I get the feeling like she wants the Organization brought down in a way that gives the boss some closure in the defeat to give up whatever dream/desire he had that prompted the whole thing in the first place. Shinichi would probably try to do it this "right way" (compared to the FBI) which is why Vermouth wants him to be the silver bullet.
All of this brings up another point. Why did Vermouth get irate with Itakura? If Itakura is part of the project she hates, then it seems she would oppose his program, or sabotage him. Maybe she was trying to do that by getting angry at him on the movie sets. Still though, why was Vermouth the one who contacted him later? Boss's orders (Tequila did get involved afterwards which supports this), or was there something personal for her there?