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First of all, let's face it, this is a rich person's problem. Poor people don't get to ask if they can morally get away with foisting their kids off on the paid help.
No, you can't. Morally justify it, that is. The LW has no particular responsibility towards this girl, as long as she's not involved with her father. Being involved with her father, she does have a responsibility towards her.
Let's go over the history, shall we? Until recently dad only had to see his inconvenient little mistake once a week for dinner. LW was happy with that and would prefer, really, to go back to those days, but the economy is in the toilet and the full-time tutor and the nanny have become extravagances. Priorities being what they are, the kid gets shafted first. Needs help with her homework? Fuck her, the inconsiderate brat. How dare she come to rely on the services that have been provided to her all her life.
The LW makes it clear that daddy will not be stepping in to help darling daughter with homework or anything else, any time soon. He doesn't have to. He has people for that sort of thing.
It seems the LW accidentally stepped into this snake's nest without really realizing that she was the closest thing to a human being within hailing distance. LW may be something of a gold digger, but I don't intend to castigate her for that - having money is good and not having it is bad, and most reasonable people would like to have lots. LW is a decent enough soul to realize that the girl needs and deserves a mother figure, and that resentment isn't a good basis for that relationship.
That said, there's more going on here than meets the eye. I've had a teen daughter and honestly I didn't examine her towels, and if I got fed up with having to do her laundry, it wasn't the panties that bothered me. Folding panties is just not that onerous a task. If it freaks the LW out enough to mention that in particular, something is up. And why the freaking out at the thought that she "still hates boys"? The daughter is a 16 year old bookworm. We've had 20-something bookworm virgins write into Salon, only to be reassured by many, many other posters that such behavior is not that rare among introverts. What we have here is the sort of woman who ends up involved with a very wealthy and much older man - almost certainly a woman who spends a great deal of time on her appearance - and a socially inept kid. Could any two people have less in common? I don't really foresee the LW having deep conversations with stepdaughter about the books she reads.
Dad is a rich creep, and LW is clearly not the Disney movie miracle stepmom who can save this family.