Is the husband entitled to recover all marriage expenses and the dowry, and what are his chances of obtaining custody of the child, if his wife requests divorce or khul’ after he committed to improving relations between them?

If a wife seeks khulʿ (divorce at her initiative, with compensation to the husband) or divorce without a legitimate sharʿī (Islamic legal) reason, despite her husband fulfilling her rights and his duties, then she is sinful due to the severe warning established regarding this. The husband has the right to refuse the khulʿ or divorce, or to divorce her without financial compensation, or to agree to khulʿ in exchange for what he spent on the marriage or more. As for child custody (ḥaḍānah), the mother has the primary right to it, unless her right is forfeited for a legitimate sharʿī reason. In the event her right is forfeited, custody transfers to the next in line. The husband may agree to khulʿ with his wife in exchange for child custody if he is able to fulfill the rights of custody.