What is the ruling of Islamic law regarding how to rectify the situation of an adulterous woman who became pregnant by her lover while still married to another man, and what is the way to repent from such actions?

You have committed several major sins: establishing an unlawful relationship with the young man, going to him after your father expelled you instead of going to your maharim (unmarriageable kin), then committing fornication, marrying without a guardian (wali), and returning to the first young man and engaging in immorality. Your father also erred by expelling you. You must leave this young man and return to your home or to some of your relatives. The born girl is your daughter and is not attributed to the fornicator, unless the fornicator acknowledges her as his, and the woman was not married. If you both repent, the young man can marry you, and the girl can be attributed to him, as some scholars have held.