Is it permissible to work for one's father in America, who sells alcohol in one of his two stores, without touching the alcohol, while refusing to work in his other store that sells cosmetics for fear of temptation?

You must honor and obey your father in what is good, but he should not be obeyed in disobedience. You have done well in advising your father to stop selling alcohol, so continue advising him while supplicating for him. Explain to him that he can provide you with a lawful job. Remind him of the religious texts that prohibit alcohol and the dangers of living in lands of disbelief. We advise you to marry, observe voluntary fasting, and lower your gaze to stay away from temptations. If he insists on you working with him and you are able to avoid selling or carrying alcohol, then there is no harm in working with him in what is permissible.