Picking up where she left off in A Game of Thrones, Cersei Lannister continues to make life difficult for anyone with the last name Stark. It's a pet project of hers.
After watching her son behead Eddard, Cersei has become the most powerful woman in the Seven Kingdoms as she takes on the role of Queen Regent, but when Tyrion comes to King's Landing as the acting Hand of the King, he becomes the first real obstacle to her rule. Worse, Tyrion is probably the only person she dislikes more than someone with the last name Stark, which is really saying something.
As the Queen Regent, Cersei becomes a little power hungry and a little brutal, and this makes for some rough times, especially if you are a peasant.
When she commissions the blacksmiths to craft armor and armaments, she says that if they do not meet their numbers she will have their hands crushed on their own anvils (16.Tyrion.63). When she hears street-side prophets decrying Jaime, she has them thrown in the dungeon (26.Tyion.9). And finally, when she learns that servants attempted to sneak away with horses during the Battle of the Blackwater, she orders them beheaded and their heads hung on a spike to warn the others (61.Sansa.24).
The moral of these examples is clear: Do what Cersei says or she will literally get medieval on you. (Especially if your income is below the poverty level. Seriously—she does not like the smallfolk.)
When Tyrion first arrives at King's Landing, he assures Cersei that she needs him to keep Joffrey's butt on the Iron Throne. Cersei admits that he is cunning but reminds him, "If I accept you, you shall be the King's Hand in name, but my Hand in truth. You will share all your plans and intentions with me before you act, and you will do nothing without my consent" (4.Tyrion.83). In other words, Tyrion can help, but Cersei wants to be the real power behind the kingdom.
This doesn't work so well for her, and the power struggle between the two Lannister children becomes the focus of much of the King's Landing-based story. Being much better at the game of thrones than Eddard Stark, Tyrion manages to negate most of Cersei's power: He removes people loyal to her from office; he makes sure most of the soldiers and sellswords are on his dime; and he even turns her new lover, their cousin Lancel, into his informant.
Tyrion effectively wins the game of thrones against Cersei, and we know Cersei loves her power, but how desperate is she to regain it? During the Battle of the Blackwater, Ser Mandon Moore attempts to kill Tyrion, and Tyrion firmly believes that Cersei put the knight up to it. "A slip of the hand here, and Cersei will be free of me" (68.Tyrion.33), he notes.
Did Cersei attempt to kill the brother she so despises? And will she regain her power now that Tywin Lannister has taken the office of Hand of the King? We'll have to wait until the next volume to find out.
One of Cersei's more enduring qualities is that she loves her children. When she discovers that Tyrion plans to send Myrcella to Dorne, she shouts at him, "Myrcella is my only daughter. Did you truly imagine that I would allow you to sell her like a bag of oats?" (21.Tyrion.91). Remember that this conversation takes place in a world where arranged marriages for daughters are as common as proms are these days—and having been in an arranged marriage based on politics and not love, Cersei no doubt wants to protect her daughter from a similar fate.
Tyrion tries to calm her, reminding her that Myrcella will be safer in Dorne where Stannis cannot "mount her head beside yours" (21.Tyrion.108). At this image, Cersei begins to cry.
Her love for her children may be heartwarming, but it is also a problem when it comes to Joffrey doing his kingly thing. Tyrion argues that the reason Cersei cannot bring Joffrey to heel is because the boy knows she will never hurt him. To which she replies—totally missing the point by the way—"If you believe I'd ever allow you to harm my son, you're sick with fever" (4.Tyrion.78). Yeah, it's safe to say Cersei's not going to be part of the solution to the Joffrey problem.
While watching Joffrey threaten Sansa for the umpteenth time, Tyrion wonders if Cersei can "truly be so blind as to what he is" (42.Tyrion.18). For the love of her children, the answer seems to be yes.
Cersei also serves as a foil for Sansa Stark. Sansa is kind, innocent, and believes in the stories of knights and their ladies; Cersei is harsh, world-weary, and believes in the coldness of reality. And like a Sith lord, Cersei feels she has a lot to teach her young apprentice.
During the Battle of the Blackwater, Cersei seems to enjoy torturing Sansa with her words of wisdom. For example, when Cersei complains she would rather be fighting with the men than sitting with the frightened ladies, Sansa reminds her she invited them. Cersei replies:
"Certain things are expected of a queen. They will be expected of you should you ever wed Joffrey. Best learn. […] Of themselves the hens are nothing, but their cocks are important for one reason or another, and some may survive this battle. So it behooves me to give their women my protection." (61.Sansa.11)
Her outlook on life might be cynical and her tone nasty, but she is teaching Sansa what is required of ladies in their social position. Should Sansa become queen, she will need to provide similar services and know why.
In another telling scene, Sansa has her period for the first time and is terrified that this means she will have to sleep with Joffrey and bear his children. We don't blame her; that's a terrifying thought. Cersei takes her aside for breakfast and tells her what childbirth was like with Joffrey. During this awkward conversation, she tells Sansa:
"[Joffrey has] never been able to forget that day on the Trident when you saw [Arya] shame him, so he shames you in turn. You're stronger than you seem, though. I expect you'll survive a bit of humiliation. I did. You may never love the king, but you'll love his children." (53.Sansa.83)
From this quote, we can clearly see that Cersei sees her past self in Sansa's current predicament. Like Sansa, she was traded into a loveless, but politically vital, marriage to become queen. She was shamed by Robert's undying love for Lyanna Stark, and she found solace in the love she had for her children. In a way, Sansa is Cersei v2.0.
Cersei may not have a tender manner or loving bone in her body (except where her children are concerned), but she is teaching Sansa how to survive the court of King's Landing all the same.