The plot twist is that there's only one daughter who's desperate for both siblings and romance, so she created an imaginary sister who also wants to do her. The mother is disturbed, but also afraid of how her daughter will react if she points out that it's all a hallucination, so she pretends to be okay with the relationship.
Less fucked up theory: One of the sisters is actually adopted, so they aren't related, but only Mom knows this, and she's too afraid to tell them the truth. But, since she knows they aren't actual sisters, she's fine with them dating.