What causes the conflict between Catherine and Linton in Chapter 23? How is the conflict resolved?

At the subject of unhappy marriages, Cathy and Linton quarrel about their families; Cathy tells him that his mother left his father, and he tells Cathy that her mother did not love her father, but loved Heathcliff instead. Cathy pushes Linton, causing a terrible coughing fit in the weak boy. Linton is manipulative, and Cathy's sweet soul falls for it; Cathy promises she will come tomorrow, even if she has to sneak over the high wall to get here.