The night before, Heathcliff came back sooner than usual because of the weather. Isabella was reluctant to let him in and was going to let him outside for five minutes, but Hindley took a more extreme measure: he wanted to kill Heathcliff once and for all.
Isabella didnt really agree, but Heathcliffs insult upon her warning changed her mind. She hoped that Hindley and Heathcliff might as well kill each other. However, Heathcliff was more agile than Hindley. Vapid Hindley ended up bleeding and unconscious. He didnt die, though.
The next morning, Isabella decided to take revenge. Heathcliff was miserable already with Catherines death. Isabella took pleasure in torturing him, saying he was the cause of her death. Irritated, Heathcliff told her to go away. Isabella first refused, but she saw that Heathcliff wasnt afraid to kill her and so did escape to Thrushcross Grange, where she was now.
She stayed only very shortly, but long enough that she earned her brothers forgiveness. After since they regularly corresponded. When Isabellas child was born, he was named Linton.
Six months after Catherines death, Hindley died. Ellen persuaded Edgar to take Hareton to live with them, but it turned out Hindley owed Heathcliff so much his son belonged to Heathcliff as well.
As for his real daughter, Edgar called her Cathy to differentiate her from his wife. He didnt want to call his wife Cathy because thats the way Heathcliff called her.