The White Queen has taken a vow.
She lives in a beautiful, serene (sterile) palace, surrounded by whiteness and lightness and quietude, and she does not harm any living thing.
Her sister, by contrast, is loud, brash, harsh, ugly and imperial. And oh, yes, she is obsessed with others' heads, especially the cutting off of them. The two of them have been at each others' throats since the day the White Queen was old enough to recognize the Red Queen as a person.
The Red Queen is fire and passion. She wants desperately to be loved and knows that she is merely feared, and so she breeds monsters of mass destruction in the hopes that one day, she can scare the people out through their fear to the other side. A semblance of love sates just as well as the real thing.
The White Queen is ice and absence: absence of blood, of fire, of warmth, of heart, of life - of anything red. She knows that she is both loved and feared, by those Underlanders who choose to see.
They are both sprung from the same stock, the White Queen and the Red; at their cores, they are the same seething sadistic monstrous ids, but whereas the Red Queen splashes her id everywhere, the White has control. She has, as she told Alice, taken a vow.
(Alice was told a lot of things in Underland. But Alice, poor, poor, innocent Alice, didn't listen. The White Queen was quite blunt with her, sitting in that kitchen holding that knife, but Alice was deaf to it all.)
(The White Queen does not kill - the White Queen has champions. The White Queen does not maim - the White Queen butters your fingers and soberly removes them, boils them into little cordials that she decants into little bottles, labels in a neat hand, and leaves around for inquisitive little Upperlander girls to find and grow smaller. The White Queen does not order - the White Queen manipulates, plays you like a fiddle, like a human, like a chess piece. Jabberwocky blood makes any dream come true - once, and then it shuts all doors to any others.)
(Alice ought to have paid more attention to the White Queen's obvious artifice, and to the hollow darkness in the White Queen's eyes.)
(One day, not long from now, Alice will wake up. She will look up from her accounts, she will go out into the bustle of the port, and she will, briefly, see.)
(She has too much sympathy for the underdog, no matter how unlike her, to not have sympathy for her fellow humans. She will realize, in one blinding brief moment of clarity, that she could have stayed in Underland, could have died to her real life and been reborn in a wondrous dream, could have stayed innocent. Instead, she has chosen to go back to the upper world, where she has done nothing but line her pockets at the expense of an entire people.)
(When Alice looks in the mirror, she sees a swollen head and red on her hands. It reminds her of something she never again remembers.)
(When the clarity begins to fade, as all epiphanies do, Alice will try to seize the moment, seize the dream, as she should have done when she was nineteen, and she will follow the ghost of a white rabbit down, down, down, to the cold, shining, white-capped sea. It is too little, too late. Alice no longer believes in impossible things, but that is quite alright, for the White Queen has always been the one with imagination.)
(The Red Queen feeds on passion. Her sister feeds on pain.)
But all she has given up, as the White Queen told the Knave, is kindness.