Is it permissible for my husband to continue his administrative work in a hotel that sometimes serves alcohol, knowing that his work is far removed from that, and that leaving it would cut off our source of income? Does this fall under the necessity that permits him to remain in his job?

The husband's earnings are permissible if his work is not involved in serving alcoholic beverages. However, if his work is related to serving alcoholic beverages, then his earnings are forbidden, and he must leave this work unless there is an extreme necessity, such as the unavailability of other permissible work that suffices to cover his basic life necessities. Once he finds permissible work, he must leave the forbidden work.