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Everyone seems to think that the LW goes and Dad/Nanny start being proper parents. Consider that the nanny is part of the problem here. The girl is spoiled rotten? Never taught basic things?
She doesn't seem like the nanny on television.
In addition, half of what everyone is considering pathology isn't atypical for teenagers.
I think the LW has some fairly rigid ideas about how the potential step daughter should behave. Some stuff isn't anyone's fault. Other things the kid will figure out if she has to. The rest is just a question mark.
The LW shouldn't live in the flat -- I agree with that. I don't think the LW ending the relationship will transform the dad. He will just find another girl friend, and muddle along with his daughter.
I will say that the LW might want to move along just because she finds dad + daughter an unattractive package deal. But if the guy is the love of your life, etc. there is no need to sacrifice in order to provide the dad with a better opportunity to do what he isn't inclined to do under any circumstances.
But if you are going to ditch the guy, it does sound sort of nobel to make the sacrifice, etc. Go for it.