What is the ruling regarding a husband reclaiming the agreed-upon dowry amount for performing 'Umrah, then refusing to go, knowing that his wife has expressed her willingness to bear the costs of her own 'Umrah?

There is no objection to a woman stipulating that her dowry be an 'Umrah (definition), as it is her exclusive right, and it is not permissible for the husband to take anything from it except with her consent and good will. If performing the 'Umrah becomes impossible for some reason, it is permissible to postpone it or replace it with money or goods, by mutual agreement between the spouses. The husband must fulfill his promise, as breaking it is one of the characteristics of hypocrites.