What is the fate of child custody if the wife seeks a Khul' (Islamic divorce) because she lives with her husband's family and he refuses to provide a separate residence, and is it permissible for her to travel to her family before obtaining the Khul'?

It is the wife's right to have suitable, independent housing, and the husband does not have the right to force her to live with his family. It is advisable to engage in calm dialogue with the husband to convince him of the importance of independent housing, and not to rush into seeking divorce or khul' due to its negative effects on the children. One should be patient and supplicate, for there is much good in patience, and "perhaps you dislike a thing and it is good for you."