Cersei is horrible at the game.
1. Sansa looks up to Cersei as a rolemodel even after Ned was imprisoned. She doesn't anymore for no other reason then Cersei decided to give up on trying to control her that way. This is not a disadvantage.
2. Cersei is the Queen-Regent, the lawful ruler on the realm. She could not stop Joffrey, a boy she had known his entire life from making the call tokill Ned, this was her fault. Entirely. She has all power she required to stop him but as Tyrion says, Joff knows she won't do **** against him.
3. Barristan is the last real hero of the Seven Kingdoms. The people look up to him. Cersei decided to break the rules and have him dismissed for no real benefit. And then he declared against them in the middle of the thronerookm and escaped the city.
4. Tyrion NEVER wanted Joffrey dead. Cersei refuses to understand this and for the sake of her children decides to kill him when he is trying to save the city.
5. Joffrey was in minimal danger on the wall of the city. Having him get scurried off to his bedroom greatly increased the possibility that thecity might fall.
Cersei has ruthlessness, no enemy she has her sights on has much hope of success while she's around because she'll go to no lengths to take them down no matter how suicidally stupid it is when looking at her own interests. Luckily she can get away with it because Tywin, Tyrion and (to a certain degree) Petyr are still looking out for her.
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When you've got a pretty-boy monkey on your back constantly calling you a puppet, you hardly want to seem like you're happy to be used. - DSakaCharanJ