It's funny how her master knows exactly how to properly punish her.
Because as long as she's not close to her master, existing itself becomes a punishment.
Putting her in places where she actually learns from the punishment is a bonus because her master is kind and sees her as a friend.
Her master: "Despite being my maid, you are also my friend and you should get along with my other friends."
Her: "No I won't, I'm just your maid."
Her master: "If so, then I remove you from the job."
Her: "Whyyyy?!?!?!?"
Also, as a maid why do you have opinions on your master's friends when they're actually good people and beneficial to boot. And why do you get jealous of the friend if you don't consider yourself a friend of your master?
She is both a maid and a bodyguard. As a maid, she doesn't have the right to question her master's taste in company. But she sure as hell does as her bodyguard.
As for why she has issues with them, its likely stemming from her being indoctrined into the typical status gap that MC doesn't adhere to. She is currently of the noble elitist mentality, seeing one's stats as being more important than their merit. Its why she questioned why Mel was there. Mel is seen as being of higher status than other adventurers in her eyes, likely on par with herself in terms of status, since she often does work for nobles too.
What she currently doesn't understand (or maybe she does but is currently rejecting the truth) is that status isn't everything. It certainly adds a significant weight to one's initial worth, but its not as all encompassing as she wants it to be.
Honestly, she would quickly fail as an actual noble if she remains as she currently is. Being incapable of giving value to those who are simply below her in status is a surefire way to drive out those who are of real value. A kingdom cannot run on status. It needs those with the ability to do the things that are needed.