[b]The River:[/b]

I see it going generally: Arya and BB are sparring, Sansa and Joffrey happen upon them. Joffrey steps in (for whatever reason) and Arya protests and says they should fight instead. He advances on her, direwolf bites him and Arya gets the upper hand. Joffrey calls for The Hound to get the runaway. He then tells Sansa and Arya to not tell his mother about the incident. Sansa wants to appease him and won't. Arya may need convincing.

I don't see Joffrey confessing outright to the event unless Sansa or Arya said something to Cersei/Ned/Robert/whoever first.

So either Cersei weasels it out of Sansa when she suspects Joffrey is hurt.

Or Arya, out of spite, confesses.

I'm leaning more toward Sansa letting it slip out. He could then downplay it as much as possible but Cersei would want payment and demand the direwolf (whichever is closer, probably Sansa's?) to die. This could get a rift forming between Joffrey and Cersei, and Joffrey and Sansa. It could also prove to Joffrey that while Arya may be troublesome, she is one to keep her word, like Ned.

[b]Clash of Kings:[/b]

Eddard reacted right away though, he did very little plotting and played right into Petyr's hand.

If we gave him time to approach Joffrey rather than make a public display which was what got him into trouble the most, we could use Ned a little better, while still being able lock him away while matters are discussed. Since Tyrion would be around King's Landing (since he's not captured) he could talk sense into Joffrey and help him cope, if he believed the truth/rumors.

If Cat traveled down to talk to Joffrey (and see her girls) it could provoke Petyr put into action the idea of smuggling Joffery and some others out of the city. He could "help" Cat by first getting Sansa out which would of course give him personal leverage with Cat, while also setting in motion the fact that Joffrey may have to wed Sansa, pre-revolts and pre-Blackwater I assume?

EDIT - it could be fun to see Cat and Cersei square off, though I am sure Cat would watch herself, but if she sees Joffrey acting on his own, she would change tactics and try him.