Does the wife deserve the full deferred dowry and all her rights, and is the husband entitled to reclaim the gold and travel visa costs, if she is the one who sought the divorce and refused to join him?

If the marriage has been consummated, each spouse has rights over the other. These include the wife's obedience and her relocation to her husband's home, enabling him to enjoy conjugal relations, and the husband's obligation to provide lodging and maintenance for her. It is not permissible for a woman to seek divorce except for a valid excuse, as the Prophet (peace be upon him) said: "Any woman who asks her husband for divorce without a sound reason will be deprived of the scent of Paradise." If you do not wish to divorce your wife and you are not at fault, you can refuse the divorce and invite your wife to khul' (divorce at the wife's instance, usually with a compensation) and to forgo the dower or gold, while considering kinship ties and not burdening her family beyond their capacity.