If Tywin had been Hand...
I think he would have put Aegon across his knees and spanked his butt for being so stupid...
shareI think the difference is that Tywin, and even Cersei, had more forceful personalities than both Otto and Alicent, so the former had much more power over their king. In addition, Aegon II seems to have a more forceful personality than Joffrey, especially with his own personal dragon to inflate his ego.
Tywin's roles was much more prominent than Otto's, since he was fighting Joffrey's battles and maintained a strong Lannister garrison at King's Landing, so it would seem that Joffrey wouldn't have had the ability to do anything to Tywin without major repercussions. I think that Tywin would have had a harder time managing Aegon II, but would have certainly fared better than Otto.
Aegon also has a dragon and is a little older than Joffrey. Otto is a second son of a somewhat more minor house (not slouches, but not paramounts).
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