In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, first of all you should know that a Muslim is a person of da`wah and always tries his or her best to set a good example for people to attract them to the straight path of Almighty Allah. In doing so, a Muslim encounters different types of people, some of whom respond to his or her call and others who do not. In one authentic Hadith, the Prophet (peace and blessings be upon him) said: “The one who interacts with people and endures their evil is better than the one who does not interact with them or endure their evil.” So, it is very natural that you get this kind of response from your aunt and that she does not get along with you. However, you should remember the Hadith of the Prophet (peace and blessings be upon him): “Al-Wasil (one who maintains good relations with his kin) is not the one who recompenses the good done to him by his relatives, but Al-Wasil is the one who keeps good relations with those relatives who have severed the bond of kinship with him." (Reported by Al-Bukhari.)
With regard to your question, Sheikh Muhammad Ali Al-Hanooti, member of the Fiqh Council of North America, answers:
“You need not cut off any relationship with people because a Muslim is created to please Allah Most High and to make da`wah. You are not created for conflict and fighting against your aunt or anyone else in your family just because they are doing something wrong. You should put yourself in the position of one who wants to attract people rather than to judge them. There is no benefit in cutting off your relation with your aunt. Maintaining communication is likely to make it fruitful, insha’ Allah.
Selatur-rahim means that you keep your relationship and help your kin.”
Sheikh Muhammad Iqbal Nadvi, Imam of Calgary Mosque, Canada, and Former Professor at King Saud Univeersity, Saudi Arabia, adds:
“Selatur-rahim means to maintain ties of kinship. It is not related to your aunt's response. You may show selatur-rahim by making du`a’ for her, visiting her, helping her whenever she needs help, and having a good feeling for her in your heart. This is the meaning of selatur-rahim in the Islamic perspective. Your aunt’s response has nothing to do with keeping good relations with her."
For further details, please read the following fatwa:
Islam’s Care for Ties of Kinship