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You are in the same house right? You are a family now. YOU moved into her life several years ago, and she is a product of how she was raised. I am afraid, you have a hand in that. Dad is clearly negelecting her and it appears you enabled him. Where are the in laws? What was up with the Nanny and what were the Nanny's instructions? How isolated is this girl? What kind of school is she going to?
Does she love you?
No she is not the popular girl on the playground. Yes she will struggle in school. She might be socially dysfunctional but people get over that all the time. People get over the white lie self-aggrandizment. (Kids do that. Even adults do that.) If she is not fashionable enough, take her shopping and limit her wardrobe to a few pieces that will match. Go for a spa day. Take her to the club and work out. Can you do these things? I think you can do these things. I think you can be, if not the world's greatest mother, at least a friend. If these are not things you are willing to do, please do her a favor and leave. You will cause more damage.
Rent "The Sound of Music." Are you more sympathetic with Maria or the Baroness?