Is it obligatory for a young woman to seek employment to support her parents, especially since her father works in something unlawful and refuses to abandon his work, and will her supplication be answered while she is eating from this money?

Working in the field of alcoholic beverages is forbidden by Islamic law, as the Prophet (peace be upon him) said: "Allah has cursed the drinker of alcohol, its server, its presser, its extractor, its carrier, the one to whom it is carried, its seller, its buyer, the one who consumes its price, and the one for whom it is bought." And because of the Almighty's saying: {O you who have believed, indeed, intoxicants, gambling, [sacrificing on] stone altars [to other than Allah], and divining arrows are but defilement from the work of Satan, so avoid it that you may succeed} [Al-Ma'idah: 90].

As for spending from this money on the wife, children, parents, and the like, there is no sin upon them if they do not have sufficient money or enough to meet their needs.

It is not permissible for the father to remain in this job except out of extreme necessity that prevents him from providing basic expenses from a permissible job or lawful money. Remaining merely to obtain full retirement is not a necessity.

The father must repent to Allah Almighty by leaving the forbidden work, feeling remorse, and resolving not to return to it. If he is compelled to stay, there is no sin upon him.

It is not permissible for the questioner to work in a mixed environment or any forbidden job to "save" her father.