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.
I gotta know, do people actually get sick from going outside in the rain or cold? Is this how disease works?
Well... If you want to know the technicalities of it, it's possible to get sick from the rain especially if it's a cold rain and if the person is also experiencing stress or something similar of that nature. Low temperature, stress, depression, etc lowers our immune system hence we've become more susceptible to viruses and bacterias under those circumstances. So it's plausible.