WV I don't think there was anything to see through with Miss Bingly. She was what she appeared to be, a reasonably wealthy young woman who needed to marry as well as possible to keep her status in society. She knew how to behave in society, and she was bitchy when she needed to be to try and deter the man she wanted to marry from marrying someone else. She wasn't like Mr Wickham who was genuinely dishonest and therefore despised by Darcy. I think Darcy just found her a bit tedious and a bit bitchy.
I reckon, after Elizabeth died, Mr Bingley and Jane came to stay to comfort Darcy and help with the children. It would only be natural, if Miss Bingly was still unmarried, that she might be living with her brother and therefore travel to Pemberley with him. Once there she would be helpful and sympathetic. It did say in P&P that both sisters were lively and amusing when in the right company. Darcy would feel that he would never feel love again the way he did with Elizabeth and would gradually notice that Miss Bingley was good company, socially adept and eager to make him happy. Feeling the need to provide a suitable mother for Elizabeth's children, Miss Bingley would seem as good a choice to Darcy as any other woman.
I reckon that she was probably, if not exactly kind and loving, at least a resonable parent to Elizabeth's children because they were also Darcy's. But as they grew older and got cheekier (they took after their mother) she liked them less. She also resented the boy (if there was one) because he was first in line to inherit Pemberley, ahead of her own son. She fulfilled her responsibilities, such as engaging a governess and presenting the daughter (if there was one) to court, but she was always cold and distainful. If they did anything she disapproved of she would call them a hoyden like their mother, but she never said that within Darcy's hearing.