[b]Clash of Kings:
[/b]
I do think Eddard was honestly upset that the incest happened as if you remember it is considered a critical sin through the religion Eddard follows (the Old Gods apparently are really against bastardy, incest, and kinslaying). So mixed with Eddard’s extreme sense of honor I think that was the reason he acted on the news of the incest so brutally. Did Petyr and Varys lead Eddard to discovering this? More or less, yeah, but his reaction was his own and not forged by the manipulation right?

I think that was the point of Robb though, he was rash and didn’t think things through (such as screwing over the Freys). Perhaps a smarter Robb would be prevalent in the AU, but I like the rash idiocy of Robb that cost him both Winterfell and his life in the long term.

I think people trying to head to King’s Landing when news that Eddard’s trial being delayed becomes apparent (and him not executed). Maybe Cat would try to go off to King’s Landing, and then it becomes a battle for who can convince Joffrey to do what with Ned (which Cersei and Tywin would want sent to the wall or exiled iirc).
[b]
The Trial:[/b]

Remember that Arya implored Sansa to tell the truth, which she doesn’t. But I’m struggling with Joffrey admitting something or keeping quiet to save his pride. If the former, I imagine it would be something along the line of: “We were sparring, it got out of hand.” obviously stretching the truth. Though I imagine it wouldn't cange much since Cersei would just be like "Direwolves are dangerous" or "Something needs to be punished".