What should a Muslim wife do about her atheist father, who drinks alcohol in her home, when she cannot leave the country at present?

If you are able to bring your wife to your place of study, then do so, out of fear for her religion and honor from her alcoholic father's environment. If you cannot, then send her to your family to live with them, because you are responsible for her. If all of that is not possible, then look for another place that combines your studies and your wife's presence. As for her interaction with her father, she must treat him kindly and dutifully, and not expel him from the house as long as his drinking does not harm her, because Allah commanded to accompany parents with kindness even if they strive to make one associate partners with Him.