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.
First of all, we congratulate you upon embracing Islam, and we ask Allaah to make you firm and steadfast on it until the day you meet Him.
You should know that Islam wipes out the previous sins as Allaah Says (what means): {Say to those who have disbelieved [that] if they cease, what has previously occurred will be forgiven for them.}[Quran 8:38]. Furthermore, the Prophet said to 'Amr : "Did you not know, o 'Amr that Islam wipes out the previous sins?" Therefore, you should continue your life as if nothing had happened and you should not take into consideration the whispers of the human devils and jinn. You should be patient on their harm as there is good in patience. For more benefit, please refer to Fatwa 88764.
We advise you to be kind and dutiful to your family and be keen on calling them to Islam according to your ability. For more benefit, please refer to Fataawa 92127, 85180, 82771 and 82279.
As regards cutting ties with them, it is permissible to cut ties with a non-Muslim in any case. Al-Haafith when interpreting the following narration: "It is not permissible for a Muslim to cut relations with his brother." [Al-Bukhari and Muslim], said: 'This narration is evidence that it is permissible to cut relations with a non-Muslim, as there is no support and loyalty between a Muslim and non-Muslim.' Rather, it is an obligation to cut relations with a non-Muslim in some cases. As-Saffaareeni quoted the statement of Imaam Ahmad which reads: 'It is an obligation to severe ties with a non-Muslim or an innovator whose innovation renders him dissolute, or a person who calls to a misguiding or dissolute innovation. Only those who are not able to refute the arguments of the above-mentioned dissolute people and innovators are obliged to cut relations with them, but those who can encounter them and refute their claims are not obliged to do so.'
Therefore, if you are safe from being afflicted in your religion and you are able to socialize with them while being able to observe the matters of your religion, like wearing Hijab and the like, and you believe that this will be a reason of softening their hearts, then it is permissible for you to keep ties with them, otherwise it is better for you to cut relations with them in order to be safe in your religion but you should be kind and dutiful to your mother as much as possible; for more benefit, please refer to Fatwa 86378.
Finally, it should be noted that it is not an obligation to keep ties with non-Muslim relatives as the Prophet said: "The family of my father are not loyal to me, as my Protector and Guardian is Allaah and the believers, but I just keep ties with them to the very minimum." [Al-Bukhari]
Ibn Hajar said: 'Al-Qurtubi, said: "This narration is evidence that there is no loyalty between a Muslim and a non-Muslim even if he is a very close relative.'
Allaah Knows best.