Choosing Wife or Mother

All praises belong to Allah, and Muhammed (SAW) is His final messenger.

Asalamualikum brothers and sisters. I have a question. I am engaged to a girl that I really want to marry. But there has been a big argument and we are trying to find a solution. She does not want me to live with my mom once we are married. I understand in Islam, once we are married she has the right to ask for a separate residence. Once married, I have an obligation to her and to my mother. My mother is ill as she is diabetic, has kidney issues, and a broken arm. She is a widow and is growing old as well. We live in America, and she doesn't speak or understand a word of English. My fiance says she does not want to live with my mom because she wants privacy. I think the issue is my family is a bit modest, and she is afraid my mom might as her to wear hijab or cover herself when going outside. I know in Islam she has a right to ask for a separate residence, but how can I leave my mother to be when she cannot provide for herself. I am in need of some guidance on how I should take actions based on the commandments of Allah, the way of the Prophet (SAW), and shariah. Jazakallah!