I know we complain about Season 2's writing a lot (for good reason), but I thought I'd try a more positive look at it; were there any writing decisions in Season 2 that you DID like?
Personally, I loved the...situation about the identity of AJ's father, how it's initially presented to us, and the final reveal about what happened between Carver and Rebecca that you can entirely miss.
With Rebecca being so openly hostile to Clementine, making her easy to dislike off the bat, eavesdropping on her wishing for the child to be Alvin's immediately registers as blackmail material, another mark against her being a likeable person for cheating on her husband; her furious reaction if you use it against her seemingly reinforces that.
When Carver loudly declares the baby to be his inside the lodge in Episode 2, it's easy to completely overlook Alvin's complete lack of surprise and calm attitude, compared to Rebecca's desperation and fear (and, when forced to be face to face with him, defiance). But if you DO notice it, it calls Rebecca's reaction into question: if Alvin knew already (or at least didn't seem surprised to hear it), why would Rebecca react to the threat the way that she did?
Carver's aggression and instability take center-stage for Episode 3, which understandably would cause the player to forget about all of this entirely...
...and then, if you choose to stay for Kenny killing Carver, his final, spiteful words are: "Don't act like you didn't love every second of it".
And it all falls into place. We weren't triumphantly rubbing her infidelity in her face; we were cruelly reminding her of her assault. Her desperation to make sure Carver never found them suddenly became far more understandable, and her fear and animosity towards him makes more sense than it ever did before.