Is it permissible for me to try to win back my fiancée and عقد قراني (perform my marriage contract) after a separation that has lasted a year and a half, knowing that she wishes to return, but her family refuses?

If a woman has been proposed to and has accepted, it is not permissible for you to propose to her, based on the Prophet's ﷺ saying: "A Muslim is the brother of a Muslim. It is not permissible for him to outbid him in a sale, nor to propose over his proposal until he (the first suitor) gives up." However, if the suitor leaves her, you may then propose to her. Your divorce before consummation is an irrevocable divorce, and a new contract is required. Remember the hadith (definition): "Choose the religious woman, may your hands be dusted," and know that a relationship with a non-mahram (definition) woman is not permissible except through a legitimate marriage.