My wife, a gyoret tzedek , brought from hu"l her elderly mother. She was alone and can’ t take care of herself. I understand my wife. But for me is really very difficult not only to share my privacy, but the mere thought of sharing my house with a goya!! I feel this almost at a physical level, ,this has stressed my relation with my wife. What can I do?

A convert is no more related to his non Jewish family and not commanded by Torah to honor his biological parents. He is still prohibited to degrade them or mock them. Nonetheless they are his parents and he owes them a great deal; as for that it is a mitzvah of Hacarat Hatov – showing gratitude, toward the parents. If your non-Jewish old mother-in-law is in no way bad influence on you, your wife or kids, it is a mitzvah to care for a lady that cared of your wife. I appreciate the difficulty in performing this mitzvah, yet the Mishnah in Avot teaches us – the more difficult the mitzvah is – the greater the reword is. All the best (Shulchan Aruch YD 241 9; Igrot Moshe YD 2 130; Yechave Daat 6 60)