There are several ways to approach a drunk and disorderly player.
Standard drunk person handling techniques. Not really on topic for this site; Google it. Wheedle them, redirect them, you know, like you'd do with a kid. Go with it. "Roll the die, you get to take a shot!" Probably best if you're all drinking and just farting around. Some RPGs are called "beer-and-pretzels" games for a reason. I assume from the way you asked the question though that it's a "serious" game.
Call the game for the evening. "I think we're all tired. Let's wrap up and pick up here next time." Might be best. My (now ex-) wife would sometimes game with us, and would usually get smashed when she did, and would for some reason always haul off and hit me in the process. It was best to just stop before it got to that point. Also see the first additional tip below.
Bull on through. The player refusing to act translates to the character not acting, and whatever happens next is the result that unfolds in the game world. "You stand there paralyzed with indecision and, oh, the wagon hits you!" (or whatever it was that was going on). More appropriate for the ornery non-drunk, but can work here too if you're all Game Uber Alles.
Beyond those tactical at-the-table tips, you might consider:
Set some drinking ground rules next time. My current gaming group drinks sometimes, and can get loud or a bit extra jolly as a result, but everyone understands that there's a courteous limit. Expectations are important - if you invite people over to watch a football game at your house, some might expect no drinking, various people will have different reasonable expectations - some might expect light drinking, and some might expect that sloppy drunk is expected. If the group hasn't clarified, then you can't really blame deviation from what the norm is in your mind.
Double-check yourself. Now in this case there's hints that the choice the player was being faced with might be inappropriate in other contexts. (From deleted comments and edits: "It was related to a liaison of sorts. A pass would lead to unwanted physical attention, and a fail would mean failure at an important session goal.") Was it really her drunkenness preventing her from going on, or was she maybe just not communicating well being offended by the game itself? There's a line between "drunk and disorderly" and "impaired and having people test your boundaries" you may have crossed here.
The rest of the group didn't step in, which may mean that either a) they're standard passive-aggressive RPG players afraid of confrontation or b) they thought that her level of drunkenness was fine and you were just being overzealous about the game over the group experience or c) they also thought, regardless of drink being involved, that you were being inappropriate. If you had one or two, you might think you weren't being drunk and obnoxious, but maybe you were. Anyway, talk to the group and figure out not all what happened that last time, but what you all want to happen next time!
If talking through the problem with him - usually the go-to answer for this type of question - doesn't work, then you have to move on to the next step: impose consequences for his behavior.
The best way to do this is to kick him out politely. Sit him down privately and say that games are meant to be fun for everyone, but he is clearly not having fun. Phrase it that way, that it appears he's not having fun - because if he really isn't enjoying himself, then he'll see your point; or he might say that he is enjoying himself, at which point you need to explain that he's acting as if he doesn't. Or, if his fun is derived from nitpicking you, he'll be forced to own up to that (or deny it, in which case again explain that his behavior suggests he isn't enjoying himself). Add that he is, in turn, making the game not fun for you. If you have statements from other players who also don't enjoy his behavior, you can add "and others in the group", but absolutely don't name names. Then tell him that since he doesn't enjoy your game, it's time for him to stop playing. Tell him his character will be dealt with appropriately, that you wish him the best, and that you hope to someday game with him again in a setting more enjoyable to you both. End the conversation there - get up and walk away if you have to.
It absolutely sucks to have to boot someone from your game, but if he's this much of a problem and you've already tried talking to him, with no success, then you can't keep him around. He will burn you out, make your game toxic to you and probably your other players, and generally ruin everyone's good time.
There are other ways to impose consequences, such as imposing an in-game penalty on him when he starts trying to control your NPCs, docking XP, or verbally chastising him ("You do not control the NPCs. Please be quiet."); however these usually feel punitive to the problem player and will probably just make things worse. But if you honestly believe that he can be convinced to stop nitpicking, you can try them. You should note that using these will probably end up being a passive-aggressive way for you to kick him out anyway, by making him so miserable and frustrated that he table-flips and walks out - not the ideal solution. It can also make your other players upset with you and sympathetic to the problem player, since it appears you're "unfairly" picking on him - so again, use with caution.
Best Answer
I can understand switching to a different character once, like, you didn't understand the system or the campaign, and you didn't realize what kind of character would be a good fit for you. But repeatedly doing it, after just a few sessions?
It's time to sit down with the player and have a hard talk.
If the player isn't getting what they want, and it's impacting the rest of the group, it's really better to not play with this person. It may be they don't know what they want, or it may be that they'd be better off playing with another group that will give them what they're looking for. But it's very clear your group isn't providing it and it's wasting their time, and for your group, wasting your time as well.