Is it permissible to give money to a woman—whom you once intended to marry—for the expenses of Umrah and to provide for her, given her difficult circumstances, while she is married and has children, and you are married and have children?

There is no legal impediment to giving charity and spending on a woman and covering her Hajj or Umrah expenses, even if this was after an unfulfilled desire for marriage. The reward may be greater if she is a relative, as the Prophet, peace and blessings be upon him, said: "Charity given to a relative has two rewards: charity and maintaining kinship ties."