Is it permissible to give charity to needy relatives discreetly, unbeknownst to the husband who refuses to give to them, especially after he authorized his wife to dispose of his money as she wishes?

If the husband permits his wife to donate from his money as she wishes, without restriction, then there is no blame upon her for giving charity to the needy, unless there is extravagance or corruption in it. It is a reminder that Allah replaces what is given in charity. However, if the wife knows that the husband does not allow giving his money to her relatives, then it is not permissible for her to do so. She should inquire about his opinion again.