TLDR: Problem player gets upset when attention is not focused on her edgelord OC 24/7, is constantly rude in-character to the only other player, has made nothing but enemies of every single NPC she's met since she's threatened most of them, never engages in the overall story-line of the campaign, and makes me feel like I'm wasting my time trying to make NPCs or design a world when all the PC wants to do is kill people, steal shit, and then moan about how tragic her life is.
Longer explanation that is mostly just me moaning about how tragic my life is:
One of my two players has a serious case of My Guy Syndrome which causes her character, the edgiest of the edgy, a Drow assassin named Lilith, to either become the central focus of the story or be completely isolated from it. When I tried to delicately explain to her what MGS is and asked her if she could tone it down sometimes, maybe don't strangle this NPC, maybe don't call the other player's PC an idiot 50 times a day, you know what her exact, word for word response was? "But that's not what my guy would do." In one ear and out the other I guess.
Anyway, I started out actually enjoying Lilith, since my friend is very good at speaking in-character. Unfortunately, this skill is utterly wasted because Lilith is completely intolerable in every way, shape, and form. I've created a vast world with (I hope) interesting NPCs and situations, but literally all she ever does is a) threaten people, b) scream at them about how stupid they are and how smart she is in comparison, c) steal shit from people who are supposed to be her allies, and finally, d) kill people for no good reason. Because, you know, assassin. This basically makes 80% of my work feel wasted or worse, ruined because she just killed this NPC thirteen seconds after his introduction.
She has basically monopolized the campaign, which is made worse by the fact that the party never does anything together. They despise each other, which probably has something to do with the fact that Luna is constantly beating down the other PC, threatening and insulting him, which is no good for his player because I know he's taking it personally (and with the crap she says, it's hard not to- she does it with my NPCs too). I always feel like I'm running two separate campaigns, one for her and one for her brother, because at any given point their characters are in two different places. At this point it feels like they're only traveling together because they know they don't want to push my threat of ending the game if they split up.
Overall, her approach to D&D can be summed up like this. I know she'd like nothing better than for me to kick her brother (the other player) from the game and continue the campaign as a one-on-one RPG for her and her alone, and I'd consider doing private sessions if I thought I could handle more than 10 minutes in Lilith-land without trying to drown myself in my dice bowl. Yeah, bad stuff is happening to her, but most of it is her own design. Meanwhile, her brother's PC has just lost his entire family recently, is suffering from chronic nightmares, and is considering taking up a fantasy cocaine habit, but he's doing it in a way that doesn't make me want to physically reach across the table and hold his lips together. Plus, he's got other stuff going on that actually relates to the main plot of the campaign. Lilith does not. The only NPC she ever spends time with is the backstory boyfriend she created to lick Lilith's boots.
Honestly, she's given me plenty of ammo to use against Lilith should I ever need to kill her off, and at this point I'm spend my lunch break fantasizing about different ways to do it. Lilith is an ex-assassin on the run from "the most powerful assassin organization" in my world and she runs around literally wearing their armor, so several people have recognized her and she seems to WANT this because it causes drama. Additionally, she recently threw a wrench in my whole campaign by springing on me the fact that she's decided Lilith cannot go to one of the world's 3 countries (it's a small world) at all because apparently she's the most wanted woman alive there. So far I've spent the majority of my session-writing trying to figure out ways to beat back this stupid narrative with a broom because it has taken over 80% of the campaign and is preventing me from setting sessions in that country. I'm starting to fix this, but it's making it hard to concentrate on literally anything else, and I know the other player, whose character is way more interesting, is losing out because of it.
My tone here is pretty negative, but she's still my friend and I feel like I'm doing her a disservice by trying to force her PC into a game that is not designed for her, but I don't know how to fix this. At this point, I'm considering ways to close up shop early and have the campaign come to an end because her being 50% of the game has become overwhelmingly stressful for me and I know the other player isn't enjoying himself either.
Edit: I should mention that we did have Session 0 where we laid out goals/expectations, and one of them was that there would be no evil characters. The other player is playing a Neutral Good Halfling Bard, so you can see why the two don't get along.