I'm a clinical psychologist, but I'll try (and probably fail) to limit the psychobabble. Also, a disclaimer: diagnosing fictional characters with psychiatric disorders is kind of silly. Psychiatric disorders are complex and mysterious classifications of human minds, and the minds of fictional characters are not real. Therefore, what I'm doing here is just loosely applying these terms to a character who simply displays the behaviors and characteristics of a particular diagnostic label that we use for real people. Unless G.R.R.M. is someone who has a perfect understanding of how the human mind works, then his characters are of course not going to really fit into our categories. I'm also using the extremes of this particular diagnostic label in order to illustrate my point. In reality, people fall on a spectrum of all personality styles, and there's a lot more gray area. But we can still have fun with it, so here we go.

Cersei is a classic narcissist. As such, she lacks the ability to truly empathize with others. Despite this obvious reality, people seem to be falling into the trap of thinking that Cersei really does genuinely love her brother and her (late) children. While she certainly says that she does quite a bit, and while her behavior may seem to suggest that she does, it is highly unlikely that such a narcissistic character is capable of true love.

If anyone is interested in a more babble-heavy explanation then I could get into object relations theory in explaining this concept, but suffice it to say, Cersei doesn't view others as real, complete people. Instead, she views them as either "all good" or "all bad" (this is known as splitting, and it is a defense mechanism). Her tendency to split is reflective of her inability to view herself as a person who has both good traits and bad traits. Most of us are able to view ourselves in shades of gray: we're capable of good things and bad things, we have strengths and weaknesses, etc. Instead of embracing this reality, Cersei must either embrace the belief that she is a worthless, damaged, and hopeless person, or the belief that she is impeccable, gifted, and perfect. With narcissists, the latter strategy seems to prevail, at least on the surface. This is why people so often fall into the trap of thinking that narcissists really think they're the best. They don't, however, even if they're not even conscious of it. Deep down, they're certain that they fall into the former category, so if they don't embrace the latter (that they're perfect), then they will be "destroyed," in the sense of facing psychological collapse. This is a way of coping with and protecting against emotional pain, hence the term "defense mechanism."

You might think that narcissists are incapable of love, since they often seem to be quite incapable of having empathy for others. You may be right, in a certain sense (although remember, we're talking about extremes here, whereas real people fall throughout the spectrum). However, there is a sort of narcissistic love in which the narcissistic person loves others as an extension of him/herself. In this scenario, the narcissistic person experiences a fragmentation of the self in which the other becomes a part of the self. This is almost always seen with family members or lovers. Rather than loving this other person as a separate entity who has their own strengths and weaknesses, the narcissistic person splits them into the "perfect" category, and considers them to be an extension of him/herself. You see this in the way that Cersei thinks about Jamie and her children. They are her blood, and they share a part of her. As such, they must be perfect, like she is. In fact, Cersei isn't even capable of loving someone who isn't herself. Her one true love in life is her twin, who looks just like her. Loving one's twin is the ultimate form of self-love, and it is sort of a perfect embodiment of what it means to be narcissistic. As soon as Jamie departed in the first season, she was sleeping with her cousin who, again, was just another extension of herself. She can't even bare to not have sex with herself during Jamie's departure.

Although this sort of love may seem like "regular" love (in that she expresses warmness towards her children, wants them to be happy, and violently looks after their interests), it is a hollow love. Just as easily as narcissistic people merged these other people with themselves, they can split them away and cast them back into the "other" position. They will then split this person to the "bad" category, and disown them. Again, this is a defense. Rather than accepting the reality that the person is capable of having strengths and weaknesses (which would mean that they are imperfect as well), they simply stop believing that the other person is reflective of themselves. After that, they may not even experience any sense of loss or mourning.

I think this is what we saw with Tommen's death. One of the questions in the post-episode poll last week was whether Cersei would have blown everyone up if she knew that Tommen was there. Most people answered "no," but I think the answer is "yes." Again, for Cersei, it's not about Tommen; it's about herself, because in her mind, she is all that exists. People are either "her," or they're "not her." At that point, Tommen had become "not her." He had joined the Faith and forsaken his family. He showed weakness, gullibility, and stupidity, and he even abandoned her. From that point on, he was no longer a part of her. The scene when Cersei saw Tommen's body was very poignant (here it is). While we had previously seen Cersei go completely hysterical at the loss of Myrcella and Joffrey, she is cold and emotionless during this scene. This is because when the former two children died, they were still a part of her. When Tommen died, he was not.

What do people think? If you agree with this assessment, what implications will this have for her character development in the remainder of the show? Or for her relationship with Jamie?

TL;DR Cersei is a narcissist who is incapable of true love; instead she loves others only due to the belief that they are extensions of herself. Given this, it isn't accurate to say that she's motivated by a love for her children or Jamie

Edit: Very surprised to see that this is now being covered on a number of online news sites. Most of the articles include my disclaimer about diagnosing fictional characters, but not all of them do. If you're going to write an article about my work here, please include that paragraph, because it's very important that people get the message that I'm not actually diagnosing a character with a psychiatric disorder. Thank you.