Is it permissible for my husband to give charity to his family, who are experiencing financial hardship, to furnish a house for their son, or should he distribute his charity to other causes?

Your husband is not obligated to give all his charity to his family; rather, he has the choice in how he expends it. It is most appropriate for him to seek what is beneficial and to ensure that his charity is directed towards what will bring him the most reward. Giving charity to family and relatives is more virtuous because it is both an act of charity and an act of maintaining kinship ties. The more his family benefits from his charity, the better and more complete the reward will be.