We open the book with Kate in a room waiting (and waiting and waiting) for her dad to show up. We feel a bit bad for Kate because it seems like her father, Lionel, is a selfish jerk-o who deserted Kate's mother and caused her to die of a broken heart. Later in the book, Kate tells Merton Densher just how devastating this experience was for her, as she remarks that "Sometimes, alone, I've to smother my shrieks when I think of my poor mother. She went through things—they pulled her down" (22.214.171.124). Daaang. As you can imagine, this family experience has left a pretty big scar on her psyche.
Despite the terrible way her father has acted, Kate finds that she can't quite give up her loyalty to him. He's the only parent she has left, and when it comes time to explain her attachment to him, she can only say, "That's all my virtue—a narrow little family feeling. I've a small stupid piety—I don't know what to call it" (126.96.36.199). That fact that she finds her loyalty stupid shows that deep down, Kate believes that love and duty are weaknesses that make it easy for people to take advantage of you. And without doubt, her emotionally abusive father has had a big impact on the woman Kate grows up to be, especially when you see how she acts toward Merton.
Kate runs the show in her relationship with Merton Densher. For the most part, Merton acknowledges and even accepts this fact, as evidenced by him saying to Kate, "You keep the key of the cupboard, and I foresee that when we're married you'll dole me out my sugar by lumps" (188.8.131.52). In other words, he feels like a small child or dog who gets rewarded as long as he does exactly as Kate says.
Kate's treatment of Merton is without doubt connected to the example that's been set for her by her dad. She's learned that there is always a dominant person in a relationship, and she wants to make sure that she's holding the whip. Kate sometimes finds Merton downright clueless. To her cynical eye, he has no idea how the world works. At one point, she even wonders about "the amount of light men did need!" (184.108.40.206) Kate's understanding of the world leads her to believe that "light" is synonymous with world-weariness. According to Kate, if you're not jaded you must be a fool. Merton has a sort of naïve goodness and honesty to him that Kate doesn't respect because—as Kate's family experience has taught her—it's likely to make him a victim.
And so with her cynical outlook and her desire to avoid the fate of her mother, Kate turns her Machiavellian tendencies up to eleven.
Kate has learned from her own Daddy how to be selfish and conniving. And she puts this family lesson to good use when she hatches a plan to make Merton rich so that the two of them can finally get married. All Merton has to do is take advantage of a dying young woman named Milly Theale. Milly is in love with Merton, and since she's dying, Kate thinks it's a good idea for Merton to marry her so that he can get all her money when she kicks the bucket. Kate makes this point not-so-subtly when she tells Merton that she and her Aunt are leaving Venice and then adds, "What I tell you. She [Milly] stays on, and you stay with her" (220.127.116.11). In other words, she's forcing him into Milly's presence so he can propose marriage to her, even though the poor girl only has months to live.
By the end of the book, Milly has passed away and nearly everyone is devastated about her death except Kate. To be fair, Kate thinks it's a shame for such a lovely young woman to have to die. But on the other hand, her message to Merton is, "We've succeeded […] She won't have loved you for nothing" (18.104.22.168).
Now we can read this quote two ways. If we're being generous, Kate is referring to the fact that loving is more important than being loved: simply because Milly loved Merton, she won't have loved for nothing. But we can also be Kate-level cynical and read this quote as Kate saying "Hey, Milly left Merton a bunch of money in her will. Ka-ching! We've succeeded. Because we got a payday, Milly didn't love for nothing."
By the end of the novel, Merton realizes that he'll never be happy with Kate unless he can find out whether she loves him for him or the money he's inherited. That's why he gives her an ultimatum: she can either have his money or him, but not both. And, being the guy who put "James" in the notoriously evasive Jamesian prose, Henry James leaves it unclear which road Kate decides to take.