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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
What appears from the question is that this woman was divorced by her husband, who did so for the first time. Being so, she has the right to live with him in the same house; and it is impermissible to turn her out of the house of her husband to the house of her father or anywhere else. She indeed was right when she refused to leave the house of her husband, due to the Statement of Allaah Almighty (which means): {…Do not turn them out of their [husbands'] houses, nor should they [themselves] leave [during that period] unless they are committing a clear immorality...}[Quran 65:1]
Allaah Almighty Gave the husband the opportunity, during the period of ‘Iddah, to reconsider his decision concerning the divorce, and Made it permissible for him to meet the woman in private, and for the woman to adorn herself for him and display her beauty in order to tempt him to take her back. Hence, if he likes to take her back, it will be permissible for him to do so with neither a dowry, nor a guardian, nor a new marriage contract, nor witnesses, and even without her consent. That is because the woman of whom the divorce is revocable is in the same position of the wife. The man then has divorced his wife once, and two pronouncements of divorce remain for him. He has the right to take her back, by word, such as by saying: "I have taken you back", or by deed, such as by having sexual intercourse with her.
This is applicable so long as she is still in the period of her ‘Iddah. However, once her ‘Iddah is over, she is considered to be irrevocably divorced, in which case, he has no right to take her back without a new marriage contract, a new dowry, a guardian, and her consent.
Anyway, we advise them to come to a settlement and return to one another for the benefit of the family and children. May Allaah Help you do what He Likes and is Pleased with.