Kill with kindness. Be so over kind to her that it almost gets sickening sweet.
Most of her problems sounds like they stem from childhood issues of not belonging. Baby talk is a sign of a tragic event as a child, that has stunted parts of her emotional growth. The "I hate" is also a sign of the same issue, just like a 2 year old who hates their peas. She is trying her best to fit in, and it's her coping method. After about a week of everyone being super accepting, she will let her guard, and be able to grow up and act like the other adults around her.
If no perceivable change is detected after a week of being overly kind to her, and she takes it all in, then most likely she has borderline personality disorder, and there is nothing you can do to cahnge that, she will consume all the extra attention you have given her and it still will not be enough.