One of the things that is never explained is why Patricia is so hell bent on destroying her sisters marriage or why she wants to bed her.
This is a very good question, and central to the point of this story. As children, Sophia was the "perfect daughter" with the outstanding GPA and excelled in sports. Patricia was complaining to Sophia about this in the first gym scene before the co-ed shower scene. L&P strongly infers Patricia was probably compared to her older sister by their mother. I can imagine, "Patricia. Why can't you be like your older sister, Sophia?"
It is clear that Patricia rebelled early, and by age 12 is high in the saddle with boys in the bed. This was also covered in early conversation between Patricia and Sophia. Sophia pushed to a near-superhuman level to achieve almost everything to please her parents and emulate their professor standards. Sophia herself became a college professor at the age of 22 (or soon thereafter). Patricia's most conspicuous achievement is managing a hotel (we do not know who gave her the job).
Patricia wants to bring her perfect sister down to her level, and she probably has other ulterior motives as well. Since Patricia confessed that her domestic sex-life was not fulfilling she seems to want a partner-in-crime (with her deflated sister.)
I hope this insight is helpful, Jack.