Well first of all, with my Joffrey being less of an arbitrary manchild it would likely affect a lot of the events in the events even before the “fight” on the river. Such as the assassin attacking Bran in his sleep would not happen, Joffrey’s bitterness at Tyrion would not be as apparent as the Imp seems to be the only male mentor in his life who gives him any attention as Robert finds Joffrey a “little monster” and is more content with whoring and hunting to an early grave. 

If we start at the river I imagine we are going to have a lot of sequence time movements to minimize filler? 

The declaration of incest is going to make Joffrey angry as all hell at everyone when that hits his ears which will further alienate him from his own mother. 

Again Joffrey’s from the start more interested in impressing Robert so his interest in swordplay is a way emulating the strength/skill of his father even though he still gets ignored which drives him to be tougher. So at the river he’s probably a bit tougher? I don’t know, maybe his intentions were to give a lesson in a sort of aggressive way—hell maybe he doesn’t even get bitten with how we end up writing the scene? 

[b]Ned:[/b]

And yes, Ned, probably will live since he basically told Joffrey the truth of his birth which while distressing was a sort of reality he has to face. I’m thinking he would send Ned to the dungeons for an undecided amount of time as leverage? I don’t know. There’s a lot of options here that could be in-depth discussions or decisions: The Night’s Watch, Essos, etc.

[b]Sansa:[/b]

The political marriage might’ve been something Joffrey saw as more his father acknowledging him but he perhaps grows worried that Sansa’s romanaticization of the royal marriage is a sign that she’s a political creature which reminds him of his mother which makes him feel uncomfortable. Sansa is said to look very fair and like her mother in her youth—which is also initially alluring to Joffrey.