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For those who are recommending that the LW break up with this man, remember that the LW might be the sanest person around. If the LW dumps the dad, quite possibly no one will take on the role of noticing what is going on in the daughter's life, and the next girlfriend could be even worse.
It's not necessarily best for the daughter if the LW leaves. Sometimes life is not perfect, it just is what it is. The LW appears sane, thoughtful, and kind. Those are wonderful qualities to have in a role model, and that's what she is to this kid- a role model, not a parent. She doesn't want to be a parent, and hasn't taken on that role before now, and it's not exactly something you can spontaneously become to a 16 year old anyway. But she can live with her and guide her as best she can. You know, two imperfect people making the best of an imperfect situation.
And besides, the LW seems to love this man. There's a chance there for happiness for both of them, and that's worth a lot. The daughter is almost an adult (though she may not act like it) and will probably be out of the house in 4 or 5 years anyway, though she might remain on the "daddy-dole".
I would recommend that the LW stay in the relationship, and see how it plays out. Get a therapist and/or life-skills trainer (they must exist). Be kind to the girl, and meet her at her level. Don't make her your life's project- the girl has to figure out how to live on her own. Think of her as an messy roommate whom you have the right to gently scold and teach.
If your efforts have a positive impact on her life, so much the better. If they have no impact at all, at least you tried. And that's more than her father, mother, or nanny have done.