Joffrey wouldn't have slapped Tyrion because Tyrion is a better man. This again has nothing to do with the game. Cersei can't undermine Joffrey in public. Ever. EVER. Especially not when he's just been crowned. To undermine him then would be to ruin everything.
Cersei plotted to have Tyrion killed
A.Because she hates his guts for killing their mother during birth and sending her daughter away. I won't act like Cersei doesn't let her emotions tie into her decisions, she is a woman after all hehehe
B.Just in case they won. Cersei knows her son is a coward, she knows he doesn't have a clue how to fight. She admits as much in an episode this season where she's discussing Jaime. She also knows Tyrion is very smart and had a plan. She does not underestimate her brother---she's the only one throughout the entire show who hasn't.
Tyrion is good. He's very good. But as of now, the order of power goes:
Cersei>Varys>Tyrion.
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Realo won gold at the Sex Olympics with a BROKEN FRIGGIN NECK.-Voltch