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First, I could not agree more with Cary's advice.
Second, I weep for this girl that this is the lame-ass father she's saddled with--and the peevish, resentful potential stepmother she's saddled with. Frankly, it sounds like the sole source of stability and nurturing in the child's life is the nanny. The nanny at least apparently feels some true affection towards her, enjoys spending time with her, etc. It's shame she can't adopt the girl; I have a feeling she's the best shot at a happy life the girl has.
Still, I actually don't blame the LW all that much; I'd probably have a hard time embracing the situation and the daughter as well. But it seems clear that the LW is projecting all of her resentment onto the girl and identifying her as The Problem, when the real problem is the boyfriend. How has he let the situation come to this? How can she not see what a piss-poor, negligent father he is being to his own child, and how can that not enrage her?
And sadly, I think it's entirely possible that the girl is more than just poorly educated and overly sheltered; given the history of mental illness with the mother, it seems reasonable that some of her disoriented, disconnected behaviors are actually indicators of mental illness. And it doesn't sound like that's being addressed at all by her parents.
Good lord, what a sad story, all around. By all means, the LW must not marry this man. But so much more is going on here, and the sad likelihood is that nothing's going to be done about it.