What does Tom Buchanan want from his wife, Daisy, and what does he want from Myrtle Wilson?
From his wife, Daisy, Tom Buchanan wants to be respected and loved. When she mocks the books he's been reading, he "glanc[es] at her impatiently." Further, when Daisy refers to him as "hulking," he objects "crossly," saying that he hates the word, even if she's joking around. As though to taunt him, she says it again. Tom speaks passionately about his belief that "the white race" has to be careful so that minority populations do not gain "'control of things.'" He seems to want to be taken seriously by his wife and by Nick, though neither seems to respect his opinions. Later, during the confrontation between Gatsby and Daisy and Tom, Tom feels utter disbelief when he learns that his wife "never loved" him; this seems to be what angers and hurts him the most.
From his mistress, Myrtle, Tom seems to require subservience. When he and Nick go to the valley of ashes so that Nick can meet Tom's "girl," Tom issues an order for her to get on the next train and meet them in NYC. He doesn't ask or care if she's free or what she wants. When she says Daisy's name over and over, after he's demanded she never say it, he breaks her nose. He wants her to be there for him whenever he wants; he wants to control her without question from her. It seems possible that he wants this from Myrtle since he cannot have it with Daisy.