While watching a streamer play Single Again recently, I came up with a theory based on a few observations. I present it here so that the forum can feel free to point out things I missed and any bored trolls call me "fucking asshole" for expressing an opinion. Mainly I think that this theory refutes some of the posts I have seen here that refers to inconsistent or bad writing, which I disagree with.
In the flashback dream sequences where Shannon is cheating on us, the reveal of the man she is with is gradual, without us learning his name, but starting from the second time we see the scene, it becomes apparent that he is known to the main character, but not close to him. Also of note, the main character isn't saying who it was as Shannon absolutely swore him to secrecy. I feel that we can assume his identity is of relative importance to the story as a whole.
If he is a character from the past, the options are limited. He looks too young to be Jessica's ex-boyfriend (Abigail's birth father) but otherwise we don't have a lot information from the visual. (late teens to mid twenties) However, we can assume that Shannon feels the identity would cause a rift with people she cares about.
It could easily turn out to be someone like a married co-worker, or the child of a family friend, and maybe Shannon is worried that the relationship would cause drama, but it seems out of Shannon's nature to care about things like that. She cares about no one but herself. All the girls know Shannon cheated on the main character, but who she was with must remain secret at her own insistence. I feel that implies that the person she cheated with would have been personally hurtful to let her daughters learn about.
What if one of her daughter's boyfriends had caught Shannon's eye in the past? Imagine Becca dated a boy and they broke up, and he comes by at some point to try and make amends, but finds Shannon home instead. I could imagine Shannon using that boy for sex. Or Lilith could have been in love with a guy, and I don't think that relationship would slow Shannon down. The main character doesn't trust Lilith's taste in men, maybe because he knows of one who cheated on her in the past.
Becca's most recent boyfriend (about a week before game start) was broken up with on good terms, and it sounds like it was her that broke it off, but she is devious enough that even that could be part of a larger plan. I could believe Becca found out her boyfriend was cheating on her with her mom, and keeping that quiet so it would not stop her from getting revenge. I actually think this is less likely as I type this, Becca would be mad at her mom for cheating on the Main Character, but an ex wouldn't matter that much to her, based on her actions.
If it was a boyfriend of Lilith that Shannon cheated with, and Becca learned of it, it would make a lot of sense that Becca would not want to be the one who tells Lilith. Lilith would apply that betrayal to both her mom and the one who brought her attention to it, and the sisters have a strained relationship to begin with. At one point Becca mentions that Lilith commits fully to her loves, and she never instigates a break-up but is always the one getting dumped. So, if it was Lilith's boyfreind, he must have broken it off with her.
In the flashback, someone called the main character before hand. He got word of a family emergency, but didn't recognize the voice. This someone would have had to know (or at least suspect) that the affair was happening, but not want to blow up everything themselves.
I think Becca must have made the call. She visits home one day, and hears the sounds of sex. She thinks, "I'll go get another peek at Step-dad's johnson." She is surprised to instead see mom with her sister's boyfriend. She is angry at mom, but doesn't want to be the one to create all the drama. Becca then calls stepdad at work, and says there is an emergency at home.
If that is correct, then Becca is pissed at mom, and feels hurt for Lilith, who she knows how to manipulate. She has been pushing Lilith into the arms of Abigail since they were in junior high. Becca decides that she could fuck the main character to hurt Shannon, but the best way to punish Shannon is to have all of the daughters fuck her ex.
Becca is now working on a multi-stage plan to get even with Shannon, on behalf of you and Lilith. She sees how close Abigail is getting with you and realizes it would be easier to get Lilith into your bed if Abigail is already there. (especially if Abby is naked) Becca offers nudges to Abby on how to seduce you, nudges you into thinking that it's OK to sexualize them with all that "I don't care if you check me out" talk, and nudges Lilith into a pseudo-incestuous relationship with Abby.
As much as Becca talks to Abby about sacrificing a pawn to get her way, it's clear that she is the grand-master of this harem.
TL/DR:
I think that the following version of past events is most likely.
Main character comes home to Shannon cheating with Lillith's (then) current boyfriend. MC confronts Shannon, and threatens to expose the affair. Shannon begs that he not let Lilith know who she cheated with. (Shannon wants everyone to know you got cucked, but doesn't want Lilith to hate her.) Becca knows though, she was the one who called you home in the first place. MC says he won't mention the boy, on the grounds that the boy break it off with Lilith. (MC wants Lilith safe, and the guy is obviously an asshole that doesn't care about her very much) Lilith gets dumped, and deals with it before the story begins.
All the rest of the tale is Rebecca's reaction and manipulations.
Still too long:
Becca is driving this harem for revenge.