As for the Abby grabbing an unknowing Becca scene: I assume the following things:
Frank didn't know at the time how disinhibited Abby gets from alcohol.
The situation was like a car accident: you don't want to look, but you can't look away either.
A lesson in moderation for Abby? They've known each other long enough, and I think if Abby had done that to a complete stranger, Frank would have intervened.
As for the scenes between Lilli and Abby: I think the two are primarily stepsisters with certain merits. Both have no problems with what they do with each other, but still they don't want to talk about it with the parents or the paternal figure. I can imagine that's awkward - almost as awkward as catching the parents doing it.
The safe approach the first time they go out drinking with Abby is not to get involved in sharing the bed with her. Later, Frank knows better and takes precautions.
Yes, Abby should definitely know better and I'm not a big fan of the scene either, but here's what I suspect: Lili warns Abby about Frank, of course those warnings are unfounded, but Lili is just very overprotective of Abby. Abby, unfortunately, knows no measure and drinks herself into a film tear and then wakes up half-naked next to her father figure. Even if she actually knows better, I think her reaction can't be blamed on her, in the heat of the moment.
But I can definitely say: Up to and including 0.12, no day ends with a forced game over but with a more or less restful sleep, either in bed or on the uncomfortable couch. I would therefore recommend to reconsider a few decisions in the first date with Drunk Abby or to look for a walkthrough.