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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If a woman is divorced a revocable divorce, she is obliged to remain in her husband's home throughout her waiting period and she is not permitted to go out except for a necessity. Also, it is not permissible for her husband to drive her out of the house before the end of her waiting period. Allaah says (which means): {…and turn them not out of their (husband's) homes, nor shall they (themselves) leave, except in case they are guilty of some open illegal sexual intercourse.}[Quran 65:1]. That is because a woman who is divorced a revocable divorce is still considered as a wife.
However, if the divorce is irrevocable, she is a marriageable woman and it is not permissible for him to stay with her in one house. If there is a religious necessity for her to dwell with him in order to foster the children because he cannot afford a separate accommodation for her to do the fostering, she can live with him on the condition of being secure from temptation and not be in seclusion with him or share the same amenities like the kitchen, the toilet and so forth. The woman should wear Hijab in front of him and observe other religious requirements in his presence. The father is obliged to provide a separate accommodation for his fostered children whenever he is able to do so.
Finally, it should be noted that one should be careful about anything that could lead to separation between the two spouses, as this leads to the breaking up of the family and losing the children. So if reconciliation is possible they should endeavour to do so.
Allaah knows best.