She sounds confused, but you should go ahead and go out with her again, but don't move fast. It's something about you she likes for her to ask a third time to go out. And even though she has a bad home, she needs comfort which could be another reason why she just want to go on a date. You don't need to be cool with her friend. If her friend is really feeling you, then she'd do anything to keep you from dating 'ol girl. So i say go ahead and go. People talking bout her shouldn't make you not want to talk to her. Outside influences ruin what could be a good thing. Just consider you and her, fuck everybody else, basically.

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