I dig the parallel affection between Chaggie and Staticdoll here by the way. "Honey"/"Darling", aw. Anyway, Charlie and Vox both delegate a task to their Best Gal here, but it doesn't take either long to start being unsure and worried about how that best gal might handle it, unfortunately with good reason. Despite Vaggie and Vel's fabulosity, it is true that both of them also create problems by being hyper-confrontational, and a little bit impulsive.

A small side note on another parallel, but Charlie and Vox both seem a bit uncomfortable with explicit sex or sexuality? When Angel takes Charlie to the BDSM joint, we see Charlie being super uncomfortable (like she is in the pilot or in general) with explicit sexuality, and Vox is also often shown being grossed out by it (Katie coming onto him, his discomfort according to Val with having sex in public, etc). It is one, kinda nice to fight that whole "horny bi stereotype" with the two bi MCs being kinda prudish; Two, interesting from a character standpoint - C&V may both come from a more repressed background, and consequently be uncomfortable with explicit sexuality, Three, that both are protective of their own bodies and big on control. Wilder sex means losing control, something C&V both don't like to do.

Going back to the trusting thing, when Vaggi and Vel both end up kind of screwing it up - like, scoring some points, like Vaggi's trust exercise working in the long run and Vel's gambit revealing to her Carmilla's role, but also creating problems in the short term like putting the staff in danger and creating tensions with Carmilla - we see how Vox and Charlie respond to their Vees messing up:

Charlie: Vaggie! No!

Vaggie: This is the only way they'll learn, Charlie.

Charlie: No, it's not. There are other ways. It just takes time!

Charlie interferes and stops Vaggi's plan and reprimands her. Vox calls Velvette to a meeting much later, and I think it's interesting that while Charlie just tells Vaggi "No, don't do it!", Vox takes the time to explain to Velvette why it would be a bad idea:

Vox: I summoned you both here because we need to discuss some of your public... displays.  Velvette, you can't just fuck with Carmilla Carmine in front of other overlords, it makes business harder.

Velvette: Well, hey, you're lucky I didn't skin the bitch. She was boring.

C&V both take a direct approach of trying to interfere with their Vees' more impulsive decisions; both of them are control freaks to some extent who have a hard time with delegating, and the fact that Vox's delegation of the meeting task to Vel went sideways probably does fuck with his ability to trust her a little bit, especially since, well...in comparison with Vaggie, Vel takes way less accountability for her mistakes.

Both Vaggi and Vel are initially defensive of their decisions and respond with angry claim that their choice was the correct one:

Vox: Our brand is perfection, remember? We cannot let ourselves look weak to others overlords or to sinners. We are above... petty bullshit.

Velvette: Well maybe, people should start sucking less!

On the Hotel's side:

Vaggie: Time we don't have! How many Exterminations will have gone by before these idiots get their shit together? How many times will we have to watch your people be killed before we make headway?

Charlie: Vaggie.

However, Vaggie then admits to making a mistake and opens up to Charlie about her choice:

Vaggie: I took charge today and it all went sideways. I'm supposed to make your dreams a reality. I'm supposed to protect you.  I'm supposed to never fail you. 

Vel, however, continues to claim that it was Carmilla's fault for "sucking" or "being boring" and that she didn't do anything wrong. Vox finally has to make her apologize to Carmilla in order to make their plans work, and when he does finally truly tell her off for this, she responds with seething anger at him.

Vox:  Besides, you did manage to fuck up the one overlord meeting I let you do on my behalf. So, uh, maybe you should reflect a little, mm-kay? 

Velvette: (growls) FUCKING MOTHERFUCKER.

Charlie, in contrast of course, tries to smooth over it and downplay to Vaggie, telling her positive things, similar to how Vox initially tries to frame it in a way that will lead Vel to feel good about herself, flatter her ego ("we are above it") though obviously way more empathetic:

Charlie: You didn't fail me. Vaggie, you're not-you're not-

Vaggie: If I can't help you, what's the point of me?

Charlie:  Vaggie, don't say that! You do so much! It's-

Vaggie: I'm sorry. I'd... I'd like to be alone for a minute.

Vox tells Velvette to reflect, Vaggi voluntarily chooses to reflect on her own. I feel like this is a potentially interesting window into Vox&Vel's relationship given the parallels - it's possible, considering how defensive she gets at the slightest sign of doubt from him, that Vel really likes Vox's validation and wants him to approve of her - not in the dad-daughter way that was originally planned, more in an equals way - but is less honest about it.

In this parallel though, it's interesting that Vaggie admits to screwing up and Vel doesn't. Given that as I said at the start, Vox and Charlie probably both have a hard time trusting people because they're such control freaks, having one of their most trusted allies handle a project in a way that's less than perfect probably does a number on them both. While Charlie has Vaggie's apology and some benefits to show for it, from Vox's POV Vel never apologizes or brings him much out of this confrontation.

All interesting set-up for Season 2. While Charlie does have more reason to trust Vaggie given how her exercise in part worked out:

Vaggie: *sighs* I'm sorry I got so crazy today.

Charlie: *grabs Vaggie's hand* No, no, I'm sorry. I'm sorry I put pressure on you. We work as a team. I guess I just thought all this would be easier, but, we'll figure it out, together. I mean, look what your exercise did for them.

It is notable that Charlie is still, in season 2, prone to trying to control things and not trusting to her friends to handle them. She has a big problem with not listening to Vaggie's advice in S2, and I think that this may have contributed a little, especially since Vaggie admits to having such a problem with needing to feel like she's helping Charlie. It kind of puts Charlie in a position to feel like she has to be independent, to not put too much pressure on Vaggie to help her in order to keep Vaggie from feeling useless. AS much as Charlie should trust Vaggie more, there's layers to her doing so that we see here.

And on Vox's side, with Vel refusing to take accountability for screwing up, it makes sense that he has a hard time trusting her in S2 and starts pushing her away. He gives her a chance to head an Overlord meeting once, it goes south and makes an enemy of the arms dealer he needs for their take-over heaven plan, and she never apologizes. While yes, he is rude and way less empathetic than Charlie, for someone with control and trust issues, that can't be good. It highlights the parallels that separate them in S2. Vaggie and Charlie are more empathetic, Vox and the Vees struggle to understand/be vulnerable with each other.

On another note, it's also interesting how the meeting sets up the bigger parallels between Charlie and the Vees as forces for change. Rewatching it I was really struck by what a vibrant presence Velvette has in this scene, compared with the other Overlords. And how both the Vees and Charlie are the ones who end up challenging heaven.

While Carmilla and co are basically accepting the status quo and just trying to navigate living under it:

Carmilla Carmine: Welcome, Hell's sovereign overlords. I've invited you all here because you represent the controlling powers of our city. Together, you own millions of souls. Souls at risk with the new Extermination schedule. *pounds fist on table* We need to discuss what can be done to minimize the impact to our interest.

The Vees want to change things:

Velvette: We found it during Extermination day. If these Holy Rollers can be killed, the game has changed. *stands on top of table* We can take the fight to them. The Voys and I have come up with a full assault plan--

As Vox puts it in "Stayed Gone", "You're looking at the future, (they're) the shit that comes before that".. The future of hell belongs to the Vees because they are future-minded. They want to actually change the nature of things, not just sit down and take it, accept their fates.

Kind of like a certain someone:

Lucifer: Come on little lady, why the frown?/In the last 10,000 years You're the first one to change this town

Charlie and the Vees are both forces for change, and it's interesting that while the other Overlords are willing to sit back and allow all this to continue in the name of protection, Charlie and Vox in their respective ways within what seems to be two weeks of dramatic effort unseat the old status quo, stop the exterminations, and send heaven running on sheer willpower alone. While this isn't to say the other Overlords aren't within their rights to be cautious (most of us would, in their shoes!), it takes people like Vox and Charlie to make change happen.