As for Becca, who arranged her mother's infidelity and is therefore the driving force behind the plot, she is absolutely in character.
Other than that, I hope we get to see things from the slumber party in Abby's side story. It would make sense, as many insiders as there seem to be around this party it would be a waste if we wouldn't find out about it.
As for Vanessa, I think as long as she's not trying to get in Frank's pants and their dynamic is purely platonic, she's probably the kind of friend that could use. I think a Frank-Vanessa scene would undermine their friendship, at least in my eyes. What would be different would be a Frank-Beth-Vanessa scene where they both focus on Beth. It's already been established in the past that there have been instances like that, so I don't see it as problematic now.
I have to say, Lilly is my highlight in this update. As Frank himself says, she has certain character parallels to her mother, but she makes quite big character leaps in her personality that surprise even Becca. And I think her conversations with Beth are definitely something she needs as well.
And I thought Abby's reaction when Lilly casually took off her sweater and was only wearing a bra on top was pretty funny. The prankster in me thinks that's a little payback from Lilly for that one time she found Abby and Frank sleeping together. The mention of Abby's rules in particular tells me that this is a bit of payback. I may be completely wrong, but I'm absolutely sure that Lilly was having fun teasing her with her own rules.
Last but not least (more or less): I think it's only a matter of time before Abby finds out about Lilly and the others. But if we take Lilith's longing as a reference, I don't think it will be until Abby's side story is published.
My only criticism is that there are a few spelling mistakes that break the immersion a bit. I don't know if it's because it's a relatively "early" version, but CNG should work on that a bit.