She has left both times. He hates her, so she doesn’t tell him about the first child. At the beginning she is trying to get pregnant. She says she can take the humiliation to save little star (her son)! Then we see a time warp and she comes back with the girl. She goes back for revenge, but then he finds out that he has two children.
The more I see these kind of dramas, the more I think female lead is also in the fault. They know male lead hates them yet crawls back to male lead's side. Why try to sleep with him when he clearly hates you? Even though there is misunderstanding, you can try to solve that first, not belittle and force yourself on him, wishfully thinking your love can change him. Their tragedy is largely their own fault.