Quote 1
[…] Miss Kilman would do anything for the Russians, starved herself for the Austrians, but in private inflicted positive torture, so insensitive was she, dressed in a green mackintosh coat. (1.21)
Miss Kilman uses her suffering as a weapon. For her, suffering conveys a political message and gives her a cause.
Quote 2
If only she could make her weep; could ruin her; humiliate her; bring her to her knees crying, You are right! But this was God's will, not Miss Kilman's. It was to be a religious victory. So she glared; so she glowered. (5.40)
Miss Kilman wants nothing more than to provoke a response from Clarissa. She wants to have all of Clarissa's privileges (and to be her, in a sense) and at the same time, she wants to destroy her – talk about a tough spot. The two women fight a war over control of Elizabeth.
Quote 3
But no one knew the agony! He said, pointing to the crucifix, that God knew. But why should she have to suffer when other women, like Clarissa Dalloway, escaped? Knowledge comes through suffering, said Mr Whittaker. (5.56)
Miss Kilman’s only comfort is in God. Going to church is her way of making sense of her own suffering.