"A practical man can always make what he wants to do look like a noble sacrifice of personal inclinations to the welfare of the community. I've decided that I've got to be practical myself, and that's one of the rules. How about breakfast?" The Pirates of Ersatz, Murray Leinster
From your question I noticed a few things. Nominally, I completely agree with @mxyzplk's answer, so this should be in the way of an addendum.
It sucks to be the leader
In a RPG, it just completely sucks to be the leader. Most players when confronted with a plan, remember about fifteen percent of it for the first fifteen minutes. But they'll certainly remember when you deviate. Leaders get no additional responsibility and no perquisites, but they get all the blame.
In the military this is mitigated with the clear distinction between commissioned and non-commissioned officers. Not least because the isolation provides both support structures and necessary emotional distance (to a degree, of course). Being "elected" leader, especially with the pack dynamics of typical werewolf games is an extremely dubious honour that I'd flatly reject.
The fact that while you may be leader in character but not dominant over the player group makes things even stickier. You need to assert authority within the realm of the narrative without actually having that authority in reality. Again, something that will cause friction and resentment any way you cut it.
Depressing environments bleed emotions into play
The world of darkness does what it says on the tin. Having played in a horror game myself recently, the iconic themes of the world of darkness do not make for "happy" or, for that matter, validating game experiences in the main. (And, if they do, it's a violation of genre.) When you are faced with the stresses of being "leader" which are compounded by the stressors of the philosophies baked into the setting, no wonder you're having a rough time.
Some solutions:
On leadership:
Fundamentally, a gaming group is a relationship. Bad relationships that do not provide validation are a drain on mental and emotional resources. When they don't work, cut them off or change them. In your case, I'd play a game that's a bit lighter in tone and focus: a nice traditional dungeon crawl or similar heroic fantasy.
I'd also reject the leader role for all the reasons I outlined above. Or, if they force it upon you, demand the perquisites and authority that is concomitant with it: they can't have it both ways.
On the group:
I've found that group character creation creates a far more cohesive group. By having entangled backstories, the group can draw upon a deeper understanding of each others' characters, creating the basis for empathy and respect within the characters, instead of the necessary simulacrum imposed by players.
By articulating desired tropes, a "palette" (as Microscope) calls it, before the game begins, you'll be able to shape the narrative of the group in directions that you want to play. This allows you to avoid the nominally depressive tropes that come default with the setting (not limited to world of darkness) and describe a source for future characters to connect with the current group. Replacement characters, if they tie into the shared narrative, will continue to maintain the tropes and social trust.
Be practical:
As players, we shape our narratives to an amazing degree. Emulate Bron Hoddan in the Pirates of Ersatz. While playing, you will be aware of the desired practical outcome that will provide validation and satisfy your personal goals. With that outcome in mind, you then frame it in terms that suit both your character's narrative and the expected narratives of the other players such that they will act to reinforce your framing and thereby your outcome. If you fight their narrative control by "being a loner," it is difficult to achieve your own goals. If you help them work as a team and appear to sacrifice nobly on their behalf while executing your own goals... the entire process is smoother and more effective.
Note that I am not saying to lie. Instead, consider the causal constructions of your actions, the explanations for those actions to be an aspect of the role * separate* from the actions themselves. By manipulating the framing as well as the actions, you can provide the necessary hooks for the other players to support your version of reality, rather than rejecting it and, by extension, you.
Postscript
Looking at your comments to other questions, you should absolutely give this group two last tries. In the first trial (of one or two games), try a heroic romp where you can be "Big Damn Heroes." Require the players who need the spotlight be leader. In the second trial (again of one or two games), try a game where players can intrigue against each other (I'd recommend Ars Magica, but then again I recommend it for most things. Most games support PvP intrigue quite ably.) If neither game provides the validation you need and the spotlight the other players need, move on. Before you do anything, take a month break, sit down, relax, and try to game with some strangers. I'm pretty sure that if you go looking for games in the chat section of this site... someone will oblige. For more on the framing problem, I'd quite recommend Rule 34 by Stross, as it describes it in a delicious narrative context.
These are all interpersonal problems rather than gaming ones. Here's how I'd handle each of them.
Same Character I'd tolerate it. Not a big fan of this kind of behavior, but it happens. I think it's a roleplaying maturity thing.
One thing I used last game might help you. I like the list of 100 questions about your character, but didn't want to overwhelm my players with homework. Instead of asking them to fill out the list I asked them all 1 question from it before each game. This worked great because it helped grow their characters as the game progressed and because it was one question at a time they actually put thought into the answers.
I bring this up because some of the questions were useful tools to differentiate the player from the character. Asking them what advice the player would give the character, how the player and character would disagree, etc, was useful for the players who were a little too close to their characters. You could ask everyone this like I did or even ask her alone.
Setting inappropriate powers I'd brainstorm with her. "No, you can't play a robot because they don't exist in the Forgotten Realms. How would you feel about a golem?"
I think the important thing here is to work with her rather than restrict her. The idea isn't to keep her from playing a robot. It's to figure out what she is trying to express by playing a robot and then figure out a setting appropriate way to express the same thing.
Since you are the party who knows the most about both the restrictions and features of a campaign setting, you're in a better position to figure out alternatives to her ideas than she is.
I also find it helpful to use book and movie examples as a good way to communicate the feel of the game you're going for. I was trying to run a gritty and dark campaign, but one of my players wrote a 5 page faery tale for her background. With her permission I altered it, but it was clear that she wanted to play a G/PG character in my R rated game. Neither of us were happy.
Since then I've told my players what books or movies inspired the game I'm planning on running. This doesn't have a perfect success rate, because some players won't read books, but it's drastically cut down the number of mismatched characters I received. If only the Game of Thrones TV show came out before I ran my GoT game, the players might not have tried to act like an adventuring party.
Finally, it is possible that a character can't be fulfilled in a certain setting or even a certain campaign. As GM you need to recognize when this is the case. In this case I'd suggest having the player shelve that character until the next game.
Multitasking Intolerable. It's one thing if she's off screen for a while, but if she's playing she should play. If she doesn't have time for the game or if she isn't interested enough to play 100% of the time, she shouldn't be there.
This is one case where I wouldn't go for the one on one conversation. It would seem like you're bullying her. I'd lay down the law in front of everyone so that it's obvious the same rules apply to everyone.
For how to approach the situation, I think it depends on what kind of multitasking the player is doing. I'm willing to be less than polite to someone who is playing video games at my table. For homework, I'd ask nicely. Homework is an obligation, video games aren't. I'd also offer that the player could skip the game session.
Sometimes players feel like game sessions are an obligation too. I had one player with anxiety issues who was getting stressed out about game, but didn't want to miss hanging out with people. The answer for him was to invite him to come hang out while we game, but have no character of his own. I let him play NPCs when he was up for it. If your player is stressed to attend session and finish homework, try telling her she can stay at the table but not play while she's doing her homework and then when she finishes she can come back in. Tell her that it's not that you don't trust her to handle both, but that it's distracting for everyone else.
Also, to clarify when I say multitasking is intolerable, I mean playing RPGs and doing something else entirely. If you're playing game and looking up spells for your next level or writing your backstory, that's fine by me. Your head is still in game mode. Depending on the game, I might even allow miniature painting, but that's pushing it. (The sort of game where I've seen that done in a reasonable way is 3.5 with long combats. When it's 30+ minutes between turns, putting another shade of red on your cloak is entirely reasonable.)
Best Answer
Since I started DMing D&D a long, long time ago, I found that the dynamics of a mixed group of male ande female players is a tad different from a one-sex only group of players. This is purely anecdotal, however, and fruit of my own experiences and by no means is representative of the general gamer population.
Note that, for the purposes of the following text, the DM is not considered a player. All of those observations were made from a male DM point of view. Also, on Brazil, sexism in game-related matters is almost non-existent, so we DMs have usually one less problem to deal with.
Onwards to my experiences!
1) All-female and all-male groups are completely different beasts.
When you DM to an all-male group, often the group takes the more common adventure, action-oriented group with some roleplay sprinkled here and there. While individually they may show interest in romance or drama-oriented games, as a group they tend to prefer the classical D&D experience. Male players also tend to be more individualistic but not outright selfish. All-female groups show more cohesive, group-oriented behavior and they show a preference for more acting instead of more action. Their roleplay is usually deeper and they tend to avoid more fights than their male counterparts. They don't necessarily seek for romance oriented games but they don't avoid it either - if it shows up on the board, they tend to embrace it more gracefully than their male counterparts.
2) Groups where only one player is from a different gender are most of the time indistinguishable from a one-gender only group when sexist behavior is absent.
When you have a single female on a male-dominated group, the female player normally conforms and behaves just as "one of the guys". You don't usually notice flirting on the table, but when it happens it is between a single couple of players, not in a more generalized manner as described on the OP. Females in this setting take on noticeably more masculine behaviors while in group - even the way they tend to sit changes a bit, with a more comfortable, laid-back posture. You can also observe them openly burping, making typical dirty jokes that males normally are famous for, and other plethora of male-associated behaviors.
When the situation is reversed - a single male in a female-dominated group - the opposite situation happens and that lonely guy becomes "one of the girls" and the experience ends up the same as a female-players-only group. Even usually macho-mode guys end up accepting "girly stuff" in this group setting - they tend to behave in a more polite and educated way, rarely do dirty jokes, and even enroll on more female-oriented roles in-game, such as maternity or romantic drama. I also noticed that a single guy in a female-dominated group is more open to experiment more feminine stuff - like hot-pink nail polish, acne creams, and even a bit of makeup - when presented the option by their female peers. I saw this happen four times already with four different male players, so I don't think it was a specific characteristic of a single player.
3) Two female players in a male-dominated group or two male players in a female-dominated group creates more tension than more mixed or more homogeneous groups.
There is an interesting effect that appears to happen when you have a group with two people of the a given gender together with three or more people of the other gender. I'm not sure why this happens, but the change in group dynamics is evident. This is something I call "queen-bee effect". It happens almost the same way for two guys in a group of females or two females in a group of guys, but the females-in-group-of-guys is way more noticeable.
When you have a setting like this one, the two players of the gender that is under-represented at the table almost always start to compete with each other for dominance. They tend to be increasingly flirtatious (females) or chivalrous (males) regarding the players of the other gender and start to push forward their ideas while putting away the ideas of their "rival". They also seem to become way more stressed out during gaming, focusing more on competing with their rival than enjoying the game by itself. This effect is somewhat harmless in males-in-female-group but can be really disruptive in a female-in-male-group.
A player sometimes enters what I call the "Queen-bee Mode", in which they try "rule" over the table and be the only player of a given gender that gets the other gender attention. Females in queen-bee mode are usually more provocative, flirtatious, and back-stabbing than they are in other group settings, while males tend to be more assertive, chivalrous, and aggressive.
What you are experiencing sounds somewhat like this - this new player is acting like a queen-bee, trying to get the male attention for herself while reducing the other female on the table (you) to a "worker drone" state. When she reinforces her sexuality, she becomes the female symbol for the group, putting a shadow over the fact that you are also a female. I'm not sure from where this behavior comes, but that usually means that she is jealous of you, not the other way around.
The queen-bee effect is especially present in LARPS.
4) Mixed groups with at least three players from each gender are way more manageable than the group setting presented in my observation #3
More mixed groups with somewhat equally represented genders tend to behave way better than a group with a underrepresented gender. In those settings, while the Queen-bee effect may exist, it is rarer and less significant. This group setting is normally more balanced and more friendly. You will probably end up with two players in the leading position of the group, one for each gender. While one of them will be the "official group leader", the other one will have as much influence as the first one, even if it is not recognized. Think about how your father and mother behaved at your home - most of time, while the father seemed like "the head" of the family, the mother had as much power (if not more!) than him during the decision making. Sure, it was an indirect, more subtle decision power, but it was power anyways.
From what I could observe, there are actually two groups in this setting: a "female group" and a "male group". Those two groups, while working together and pushing forward towards the goal of the adventure, seem to pack up differently while making decisions both out and inside the game. Normally, the male lead-player will give a suggestion and will be backed up by the other male players, while being confronted by the female leader which is in turn backed up by the other female players. In a sense, this setting seems more like DMing to two homogeneous groups that happen to work together instead of a single, heterogeneous supergroup. As time passes, however, the groups will mingle up and become more cohesive, more intense friendships will develop, and you'll end up with a healthy, diverse group of friends.
Heck, you may even end up forming real-life romantic couples with a setting like this. For some reason, role-playing being in love with someone can sometimes have a weird reflection on real-life and you end up actually being in love with someone.
Well, that's how I ended marrying my SO, at least!
The Bottom Line and What You Should Do
You can do two things, in this situation, but first you need to understand why she is doing what she is doing. She probably doesn't even realize that what she is doing isn't really nice to you. So, my first recommendation is to talk to her. Not to discuss this and ask her to change, but in a friendly, open way. Even giggle a bit while talking to her. Put her behavior on the spot, but in a lighter tone. Comment about how it is funny, some of the jokes and all, but tell her that you are not used to it and sometimes feel uncomfortable. Always keep the light tone, however. Show her that this behavior of hers is making you feel vulnerable, and a bit alienated. Approach her as a fellow human and as a potential friend. Try to change a bit of the rivalry she has with you to friendship. If she understands that you - her potential new friend - is feeling a bit bad because the way she behaves, she may very well tone it down a bit. Don't expect it to disappear - she's a queen-bee after all - but it may very well become way more manageable.
Failing that, open yourself to your DM. Tell him that she is making you uncomfortable but you want to keep playing with them, make the suggestion to start a second group without her, on a different schedule. It may even be just you, another player and the DM, or even you and the DM.
He may very well accept that - smaller groups are easier to manage and you can create deeper, more interesting tales that way.