If Tywin was there

[Malakai Kahn]

If Tywin was present for Ned's 'confession' how would he have stopped Joffrey after he gave the execution order? I doubt Tywin would want to override his grandson the king so soon after he took charge in front of a huge crowd of people. Sending him to bed in private is one thing, but he won't want to make Joffrey seem weak in front of the smallfolk with 2 other kings vying for the throne.

[King Tyrion I]

He wouldn't have stopped Joffrey.

 

There was the crowd, there was Cersei, and there was the King. Stopping Joffrey at this time would have been capital treason.

[spndn22]

He would just tell him it was wrong after everything was already done, there was nothing to do there, ned would've died anyway

[Abdallah]

Tywin wouldn't of let Joffrey talk. He would have simply said "Ned Stark, for the crime of Treason i sentence you to exile at the wall." or he wouldn't of even done that. he would have kept him in a cell, and used him to broker a peace with Winterfell and Riverrun. 

[Heartofwinter]

While it may have been hard for him to stop him, he still could have. Plus Ilyn Payne's allegiance would appear to be much closer to Tywin than it would Joff. Enough of a pause and maybe Tywin would have sent him away. Tywin doesn't care if there is a crowd or not, plus it makes him look even more powerful, and no one cares about Joff's power yet anyway.

[Bellatrix Stark]

Tywin would have stopped Joffrey. Tywin was the de-facto King, and said himself that Joffrey needed to be controlled and essentially not giving free reign like he presently was. 

[DominusNovus]

"In the interests of the safety of the royal person, the regency has decided that it is best for His Grace, King Joffrey, to kept as far away from such a vile traitor as Eddard Stark.  I shall execute the King's Justice in his place."

[Lord Wraith]

Provided Tywin was acting Hand I think he would have.

[Lion of the West]

I also think that Tywin would have come up with a way to either stop Joffrey or in some way counter his stupid orders, or just ensuring that Joffrey said what Tywin wanted.

[Universal Sword Donor]

1) Tywin never would have bothered to announce it in public. Everyone still thought Joff was Robert's son except Stannis (or didn't care). He'd have brokered a peace and sent him to the Wall (maybe even back to WF) keeping Sansa and Arya  as hostages

 

2) If he couldn't He simply wouldn't have had Ilyn Payne come to the confession. Doubtless that Joff would have had the courage to say anything with him there. Slynt definitely wouldn't have had the balls to.

[dornishdame]

1) Tywin never would have bothered to announce it in public. Everyone still thought Joff was Robert's son except Stannis (or didn't care). He'd have brokered a peace and sent him to the Wall (maybe even back to WF) keeping Sansa and Arya  as hostages

 

2) If he couldn't He simply wouldn't have had Ilyn Payne come to the confession. Doubtless that Joff would have had the courage to say anything with him there. Slynt definitely wouldn't have had the balls to.

 

I agree. The public confession was a theatrical that Tywin would never have allowed.  At most, Tywin may have ordered Ned to come to Court and confess and then announced that the Small Council - in conjunction with King Joffrey - had determined that he would spend the rest of his life in exile at the Wall, with Sansa and Arya remaining at Court as hostages.  Cersei leaves the door open for Joffrey to get his own way - Tywin would have made sure it stayed shut. 

[CJ McLannister]

Yes.  Tywin knows how to do political theater without any great risk, and we would have made damn sure that Joffrey knew exactly what he would need to say, if anything.  That's what Cersei (et al.) should have done, but she assumed that Joff would follow her wishes.  Also, if, in fact, Littlefinger was pulling the strings behind the scenes to make sure Ned was shortened, I doubt he would have had the balls to try it with the risk of Tywin finding out about his plan.