My question is that I've cut all contact with my sister and her daughters because her older daughter became pregnant a non-Muslim man and she never been married to him. My sister knew everything but she didn't care still don't pay Allaah in anything,

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

All the Muslim scholars agree that keeping ties with kinship is an obligation. Allaah says (which means): {And fear Allaah through Whom you demand your mutual rights and do not cut the relations of the wombs (kinship).}[4:1]. To fear Allaah means to obey Him, and to be considerate about the kinship means not to cut relations with family members. Even if one's kin are not Muslims, he still has to keep ties with them. It is reported that Asmaa' asked the Prophet said: "My mother came to me hoping to benefit from me, but she is not a Muslim, shall I maintain ties with her (i.e. by giving what she wants)?" The Prophet replied: "keep ties of kinship with her." So if a non-Muslim deserves to be treated in this manner, then it is more appropriate to keep ties of kinship with a dissolute Muslim. The evidence about the obligation of keeping ties with disobedient or dissolute people is that the Prophet said: "The person who perfectly maintains the ties of kinship is not the one who treats them equally as good, but rather it is he who persists in doing so even though others have severed the ties of kinship with him." [Al-Bukhari]

A person who severs the ties of kinship is considered a dissolute person, however, the Prophet ordered us to keep ties with him. Nonetheless, if cutting relations with a dissolute relative will deter him and bring him back to the obedience of Allaah, then it will not be forbidden to sever the ties of kinship with him.

Al-'Iraaqui said: 'The scholars of our school [Shaafi'ee] and others said that this is in relation to cutting ties without a sound religious reason. However, if there is a sound religious reason, because he is an innovator, or dissolute and the like, or there is a benefit when we end relations with such people, then it is not forbidden. The evidence for this is that the Prophet cut relationship with Ka'b Ibn Maalik and the other two companions and forbade the companions to talk with them. Similarly, our righteous predecessors used to end relations with others when there was a sought benefit.'

Therefore, if there is a benefit in severing the relationship with your sister and her daughters, i.e. if this will deter them and prevent them from committing acts of disobedience, then you may sever the ties with them. Likewise, if you fear that the members of your household will be affected by them, you may also cut the relationship with them. However, if you do not expect a religious benefit, then in principle, you should keep the ties of kinship and continue to advise your sister and her daughters making use of Islamic tapes and beneficial books while dealing with them in a soft manner, may Allaah guide them to the straight path.

Allaah knows best.