Cersei, like all the Lannister brood, seems to have serious daddy issues. Her driving force during all her plotting and scheming was accompanied by "wouldn't father be proud?", or "I handled that problem just as well if not better than father would have" or other similarly paraphrased notions. Instead of making good decisions for herself and Tommen, she seems to be more motivated by surpassing Tywin's greatness, perceived or otherwise.
And even throughout ADwD, Tyrion is still haunted by Tywin's ghost and the unknown fate of Tysha - "Where do whores go?"
It seems to me that Jaime was the first to truly break the chains of his dead father's will and start to write his own personal destiny.