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I'm autistic (with a father, aunt, first cousin, and many friends that are too) and spent several years focusing on learning everything I can about "our kind." One thing I learned is that there's a stereotype about us (introverted fantasy-lovin geeky bookworms that don't bathe, etc.) and only a fraction of us are like that.
I do see signs of severe neglect and isolation in the girl. Kids learn to care about their appearance & hygiene expressly because they want to impress certain peers -- parents end up instructing, pushing & reminding them about it all the way until that point.
What I don't see, though, is a mention of certain key autistic spectrum traits. She didn't say that the girl moves a lot (or moves one body part a lot), seems to have difficulty getting moving at all, has a very strong or weak sense (i.e. hearing or touch), is prone to emotional meltdowns, has unusual speech (i.e. odd sentence structure), makes staring or avoids eye contact, seems to only talk & think about a couple of topics almost all the time...
Things like those (not all at once or limited to those) are so common that even a short description of one of us usually mentions at least a couple.
As for what the family should do... From articles I've read, I think a modern boarding school would be perfect for the girl's situation. Dorm friends become lifelong 'family', teachers/staff are like parents, independent life skills are taught & expected... She sounds like a bright girl, just one needing a lot of guidance and time with her peers. It sounds like the nanny would be happy to have her stay during school breaks, too.
Assuming the girl goes off to school, LW & partner might as well marry. Just for the sake of all involved, LW, recognize that you're both childfree by nature: giving birth will not magically make you empathic or turn your boyfriend into a good father, it will just put a strain on your relationship and produce another messed-up child.