Is it permissible to give zakat to relatives, knowing that the husband is aware of their financial situation and has said, "Your father is employed"?

You may give your husband's zakat to your father if he is eligible, because an agent for distributing zakat may give it to eligible relatives. It is a condition that your father be among those your husband described as "in dire need and their circumstances are poor." If he is not, then you may not give him from the zakat. You must distribute it to those your husband specified with that description, because an agent acts according to the principal's instructions. In any case, if you wish to give your father some of your husband's zakat, inform your husband of his need. If he permits you, then give it to him; otherwise, do not.