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.
The jurists established that a husband is not obliged to provide accommodation for his wife who is irrevocably divorced from him. However, if this divorcée (his ex-wife) fosters his children and she has no accommodation, then in this case, he is obliged to provide her with accommodation. The accommodation is a part of maintenance, and the maintenance of those children is an obligation upon him.
Nevertheless, she is not permitted to live with her divorcé [ex-husband] in the same house as she has become a non-Mahram for him, and because this leads to many prohibited matters such as mixing, looking at her and other prohibitions. Indeed, the Prophet, sallallaahu ‘alayhi wa sallam, said: “Beware, a man must not spend the night in the house of a woman who has been married unless he is her husband or her Mahram.” [Muslim] However, if the house is spacious in a way that she can be in a part of it that is separate with its amenities, then it is permissible to allow her to live in it.
As mentioned previously, the father is obliged to spend on his young children who have no money, while the mother is not obliged to spend on them. Moreover, she is permitted to ask her husband to reimburse her for the expenses that she has spent on her children in the past if she did not spend it on them as an act of charity. For more benefit, please refer to Fatwa 85012.
In any case, if it is possible Islamically and according to the customs that the two spouses reconcile and reunify their family and take care of their children and bring them up in a good way, then this is something advantageous and better in the end.
Finally, it should be noted that if a husband has divorced his wife an irrevocable divorce with a minor separation (i.e. the first or second divorce) and her waiting period has expired, it is not permissible for him to take her back except with a new contract. For more benefit on the kinds of divorce, please refer to Fatwa 82541.
Allaah Knows best.