All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
You are not obliged to let your sister stay in your house, and you are not obliged to obey your mother in this regard. However, our advice to you is to obey your mother and let your sister stay in your house as long as this does not harm you. Verily, obedience to your mother and making her happy yields a great reward.
Al-Qaraafi wrote, “A man said to (Imaam) Maalik, ‘O Abu ‘Abdullah! I have a mother, a sister, and a wife. Whenever she sees something with me, she says, 'Give this to your sister.' If I do not do so, she curses me and supplicates Allah against me!’ Maalik said, ‘I say that you should avoid making her angry and save yourself (from her wrath) by whatever you can give her.’” [Anwaar Al-Burooq fi Anwaa’ Al-Furooq, 2/93]
You should know that forgiving those who wrong you is a noble trait and a means to earn the forgiveness and pardon of Allah, the Exalted. He says (what means): {...and let them pardon and overlook. Would you not like that Allah should forgive you? And Allah is Forgiving and Merciful.} [Quran 24:22]
The Prophet, sallallahu ‘alayhi wa sallam, said, “...Allah increases the honor of one who pardons.”
For more benefit, please refer to fatwa 84351.
Allah knows best.