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 is His slave and Messenger.
Islam gives very significant rights to the parents; Allah ranks them as immediately following His right. Allah Says (what means): {Worship Allah and join none with Him in worship, and do good to parents…} [Quran 4: 36] Allah also Says (what means): {And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents…} [Quran 17: 23]
Allah enjoins being obedient to them even if they are non-Muslims; Allah Says (what means): {And We have enjoined on man (to be dutiful and good) to his parents. His mother bore him in weakness and hardship upon weakness and hardship, and his weaning is in two years give thanks to Me and to your parents. Unto Me is the final destination. But if they (both) strive with you to make you join in worship with Me others that of which you have no knowledge, then obey them not, but behave with them in the world kindly…} [Quran 31: 14-15]
Asmaa’ Bint Abu Bakr said: “My mother came to me during the lifetime of the Prophet and she was a pagan. I said to the Prophet (seeking his verdict): my mother has come to me and she desires to receive a reward from me, shall I keep good relations with her?” The Prophet said: “Yes, keep good relation with her.” [Al-Bukhari and Muslim]
A mother is given preference over a father in having good shown to her as narrated in a Hadeeth that a man came to the Prophet and said, “O Prophet of Allah! Who is more entitled to be treated with the best companionship by me?” The Prophet said, “Your mother.” The man said, ‘Who is next?’ The Prophet said, “Your mother.” The man further said, ‘Who is next?’ The Prophet said, “Your mother.” The man asked for the fourth time, ‘Who is next?’ The Prophet said, “Your father.” [Al-Bukhari and Muslim]
Therefore, you should know, dear brother, that you should not cut your relations with your mother even if she has abandoned you and your brothers and sisters. You should keep good ties with her, take care of her and be in touch with her.
As for her children from other than your father, they are your brothers/sisters from your mother’s side. Hence, Allah has allocated for them a fixed portion in the inheritance. You have to keep good relations with them even if they cut relations with you. The Prophet said: “The person who perfectly maintains the ties of kinship is not the one who does it because he gets recompensed by his relatives (for being kind and good to them), but the one who truly maintains the bonds of kinship is the one who persists in doing so even though the latter has severed the ties of kinship with him.” [Al-Bukhari]
Moreover, Abu Hurayrah narrated that a person said to the Prophet : “I have relatives with whom I try to keep the ties of relationship but they sever relations with me; I treat them kindly but they treat me badly; I am gentle with them but they are rough to me.” He replied, “If you are as you say, it is as if you are feeding them hot ashes, and you will be with a supporter against them from Allah as long as you continue to do so.” [Muslim]
Allah knows best.