By acting out on their homosexuality your cousin and her partner are doing something that you know is offensive to God. How can that not make you feel uncomfortable? There is no bigotry in this! It is perfectly OK - even necessary - to judge behavior and to feel uncomfortable around others whose behavior you know to be immoral.
The Catechism of the Catholic Church (CCC) informs us that “homosexual acts are intrinsically disordered” (CCC 2357). And while the Church calls us to accept those who suffer from homosexuality with “respect, compassion, and sensitivity” (CCC 2358) it also clearly teaches that, “under no circumstances, can [homosexual acts] be approved” (CCC 2359).
You all are in our prayers.