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I think there is something to be said for the LW sticking this one out, at least for a few more years. Not for her sake, but for the sake of a teenaged girl who has already been abandoned by two parents. The LW has been with the boyfriend five years. Long enough for the child to form some attachment to her. The LW is now reaping the benefits of a relationship that she herself helped sow - she stood by and allowed the girl's father to skate by with a meager committment of one dinner a week, foisting his child upon the nanny, taking no personal interest in her care, upbringing, or eduction, all because it was the most convenient for the LW. Is anyone surprised the child isn't self sufficent? And now that the seeds have started to flower, the LW wants to bolt? Shame on her. She's been the girl's de facto mother for five years, regardless of whether there's a piece of paper to confirm the relationship. She's done a crappy job of step-parenting - and that's what she was, whether she wants to admit it or not - and she needs to step up to the plate in these final crucial years.
The LW is lucky, in my opinion. She hasn't described any behavioral difficulties in the girl. No screaming, beligerent attitude, or substance abuse was indicated. In fact, the girl is an avid reader, which indicates an interest in learning, the creative arts, etc. What the girl needs is the devoted attention of her father and a mother figure, and perhaps some professional help to learn the more common sense things she hasn't been taught. (I wouldn't worry so much about the education - at this point in her life, the child is more likely pre-occupied by her emotional issues, and all the tutors in the world will not help. There will hopefully come a time, when she sets some occupational goals, that her interest in learning will trump whatever other garbage is going on in her life and she'll embrace eduction full force, but I don't think that time is now.)
If the LW abandons this girl now, it's not likely that the father will ever get it together enough to be an effective parent to this girl. And it's probable that the girl will never recover from yet another rejection from a mother figure. But. If she embraces the situation, seeks outside help in bringing the dad up to speed and teaching the girl the skills she needs, I think she'll find that her aggravation will fade with each success. And if there is no success, well at least then she'll be able to sleep at night knowing she did the best she could.