All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The matter is as you mentioned that sitting on a table where wine is served is not allowed. See Fataawa 85631 and 84239. So, it is not allowed for you and your fiancé to sit with his father while he drinks intoxicants and it is not a necessity. Know that if this man is only your fiancé and the marriage contract has not been completed yet, then going out with him or with his father or sitting with them is forbidden as neither of them is a Mahram (i.e. a spouse or a person whom one is permanently prohibited from marrying due to suckling, marital, or blood relations) for you unless you get married to your fiancé Islamicly. However, if his father is a Mahram such as your uncle, then it is allowed for you to be with him. See Fatwa 84300.
This man should be advised kindly and softly, it is better that this task is carried out by one to whom he may listen, such as a noble person, a relative, or a close friend. His son should apologize to him nicely and pleasantly if he invites him for a dinner that consists of any sin. Finally, all goodness lies in supplicating Allaah for his guidance and righteousness.
Allaah Knows best.