[b]Joffrey & Arya:[/b]

That is a very good and interesting point. I didn't think your portrayal of Joffery would change the events with Bran but that is a good thought. If he and Tyrion are on better terms, it would change how Tyrion is hunted in the first season, so at any rate, a war might not break out in the future, or if one does, it's for another reason.

If we wanted the rumors to hit before the river (say en route to King's Landing still) there could just be people talking about rumors. And if Joffrey, Sansa and possibly Arya overhear, it would change the dynamic between them and how Joffrey is struggling to keep himself calm while faced with a horrible truth. If we want Robert to be less drunk (only slightly so) and more of a decent father figure, we could always say he asked Syrio first, to train Joffrey. So when Syrio trains Arya, they could have that connection.

I assume if the direwolf still shows up, Joffrey wouldn't be able to get the better of it, especially with Sansa yelling at him to not hurt her pet. Arya would take plenty of pleasure of knocking Joffrey down and taunting him, even more so if we wanted them to hear rumors a few scenes before? Or that could just add too much fuel to the fire, and we could wait on that.

[b]Ned:[/b]

Ned did offer to take Joffrey under his wing, I could see Joffrey reacting to lock him up but at the same time, he must be smart enough to see Ned as a useful tool, rather than a figure which needs to be put in his place.

[b]Sansa:[/b]

Sansa bearing too much like Cersei, should be a red flag to Joffrey.

If it wasn't his choice to wed Sansa and if he's weary of her entertainment value (he sees how strained Cersei and Robert are surely) he could want to call it off. Not just too piss off his mother but for his own sake. If he wants to make his father proud, he would marry her but when Robert dies, it would give Joffrey the push to make up his own mind.

[b]Petyr & Cersei:[/b]

With Joffrey pulling away, I could see Petyr wanting to take advantage of this weakness, while his intentions are purely selfish, he may still be of use in the city, and he could always try to steer Joffrey in the (wrong) direction he likes, though if that were ever the case, I'm sure something would happen to make things difficult because seeing the genius squirm can be such fun.

[b]Tyrion & Cat:[/b]

If we don't have Bran become a cripple, Cat doesn't need to go to King's Landing, therefore she could defend Winterfell when Theon came to take over. We could keep Tyrion in King's Landing or we could put him somewhere else.