All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Khul’ takes place as one irrevocable divorce as we clarified in Fataawa 88502 and 88375. Therefore, if the husband initiated divorce to his wife after it [Khul’], this divorce does not take place because there is no relevance here, since this woman is no longer his wife; this is the view of the majority of the scholars .
However, Imaam Maalik is of the view that if Khul’ is followed by uttering divorce without interruption after the utterance of the word Khul’, then divorce takes place (because in this case it indicates that the husband intended two divorces when he uttered Khul’). This is in regard to your first question.
As regards your second question, the answer is that if the parents threaten to cut ties of kinship with their daughter or drive her out of the house if she does not sign the paper of Khul’, then this is not considered a state of constraining compulsion. So, if this husband initiated Khul’ and the wife gave him compensation, then the Khul’ is valid. In this case, the wife becomes irrevocably divorced from her husband.
If this is not the third divorce, and the two spouses wanted to turn back to marital wedlock, then her husband may take her back but with a new contract. If her guardian refuses to marry her off, she may take her matter to a Muslim judge, or whoever acts on his behalf, so that he will order him to marry her off or that the judge will marry her off himself.
Allaah Knows best.