How to deal with sinful families
Question

                What can a woman do, if her family are obstructing her path to Islam.  They are non-Practicing Muslims.  How does she fulfill sunnat ir rahim and follow Islam if there is a great deal of difficulty in doing so.  Can a sister just break ties, live on her own and try to get closer to Allah.  It is becoming difficult to maintain ties of kinship when there is continuous evil, backbiting, fitnah, inciting me to  disobey Allah, etc.,

Is there a dua to make when one faces such great difficulty?

And what do I do if I make mistakes and fall in sin – despite not desiring to do so?.
Praise be to Allah.We say to this Muslim sister: may Allaah 
    reward you with good for adhering to Islam, and we ask Allaah to make you steadfast in Islam and to send you people who will help you to do so.  
With regard to the question: 
Firstly, you have to bear their annoyance 
    with patience, because the path of adherence (to Islam) is not easy, but it is the path of the Prophets. The Muslim is bound to face difficulties 
    in the way of his adhering to Islam, as Muslim narrated in his Saheeh (2823) from Anas (may Allaah be pleased with him) that the Messenger 
    of Allaah  (peace and blessings of Allaah be upon him) said: “Paradise is surrounded with difficulties and Hell is surrounded with desires.” 
    The Prophets (peace be upon them) were faced with difficulties from their people and from the closest of people to them, but the reward for their 
    patience was that Allaah caused them ultimately to prevail. 
Secondly: 
The Muslim sister should strive to advise her 
    family with kindness, wisdom and beautiful preaching, and she should not despair or give up. She should show a good attitude towards them, say and 
    do good things to them, and extend a helping hand to them, even to those who cause her the most hardship. This will have an effect on them, in sha 
    Allah, and this is one of the most effective ways of calling people to Allaah.
Thirdly:
 She should try to find people to help and 
    support her, by trying to persuade those among her family members who like her, because they will be more likely to respond than others. 
Fourthly: 
You have to equip yourself with the most 
    effective “weapon”, which is praying for them to be guided and that Allaah will fill their hearts with the light of adherence to Islam. You should 
    say such du’aa’s a lot when prostrating and during the last part of the night, and at other times when du’aa’ is especially recommended, and you 
    should not try to hasten the response.  
Fifthly:
 You should note that it is not always good 
    to break off ties. In some cases, when those whom Allaah has guided break off ties with their families, this makes them go further in their sin 
    and farther removed from religious commitment. Breaking off ties may cause a person distress and make him unable to bear it. Hence we think that 
    the sister should be patient and mix with her family in ways that will not affect her religious commitment and level of faith. The more she 
    withdraws into herself –i.e., at home – the better, because if a woman leaves the family home, that may make people talk badly about her a lot, 
    and evil-minded people may try to approach because she has gone away from those who could take care of her and protect her. 
Your staying may be more beneficial to your 
    family, because there are many sins that the family may not dare to commit out of respect for their children whom Allaah has guided. If the 
    children leave, this will give the family more freedom to commit whatever sins they want. 
Hence the daa’iyah should be wise and should 
    weigh up the pros and cons of leaving. He should not give a small benefit precedence over warding off a greater evil; warding off evil is more 
    important than gaining benefits. 
Sixthly: 
There is no better du’aa’ for such situations 
    than the du’aa’ of the Prophet  (peace and blessings of Allaah be upon him) when he prayed for his people to be forgiven and guided. 

    (a)
    It was narrated that ‘Abd-Allaah ibn Mas’ood said: It is as if I can see the Prophet  (peace and blessings of Allaah be upon 
    him) telling us the story of one of the Prophets whose people beat him and made him bleed, and he was wiping the blood from his face and saying, 
    “O Allaah, forgive my people for they do not know.”
 (Narrated by al-Bukhaari, 3290; Muslim, 
    1792). 
Al-Nawawi said:  
The Prophet referred to is one of the earlier 
    Prophets. Something similar happened to our Prophet  (peace and blessings of Allaah be upon him) on the day of Uhud. 
(Sharh Muslim, 12/150) 

    (b)
    It was narrated that Abu Hurayrah (may Allaah be pleased with him) said: Tufayl ibn ‘Amr al-Dawsi and his companions came to the 
    Prophet  (peace and blessings of Allaah be upon him) and said: “O Messenger of Allaah, (the tribe of) Daws have rebelled, so pray to Allaah 
    against them.” The people said, “Daws are doomed.” But the Prophet  (peace and blessings of Allaah be upon him) said: “O Allaah, guide Daws 
    and bring them to me.”
(Narrated by al-Bukhaari, 2779; Muslim, 
    2524) 

    (c)
    It was narrated that Abu Hurayrah said: “I used to call my mother to Islam when she was still a mushrik. I called her one day and 
    she said something about the Messenger of Allaah  (peace and blessings of Allaah be upon him) that I did not like to hear. I came to the 
    Messenger of Allaah  (peace and blessings of Allaah be upon him) weeping, and said, ‘O Messenger of Allaah, I have been calling my mother to 
    Islam and she refuses. I called her today and she said something about you that I did not like to hear. Pray to Allaah to guide the mother of Abu 
    Hurayrah.’ The Messenger of Allaah  (peace and blessings of Allaah be upon him) said, ‘O Allaah, guide the mother of Abu Hurayrah.’ I went 
    back, feeling optimistic because of the du’aa’ of the Messenger of Allaah  (peace and blessings of Allaah be upon him). When I came back, I 
    went to the door and found it locked. My mother heard my footsteps and said, ‘Stay where you are, O Abu Hurayrah.’ I could hear the sound of 
    water. She washed herself (did ghusl), put on her chemise and quickly covered her head with her head cover, then she opened the door and said, ‘O 
    Abu Hurayrah, I bear witness that there is no god except Allaah, and I bear witness that Muhammad is His slave and Messenger.’ I went back to the 
    Messenger of Allaah  (peace and blessings of Allaah be upon him), weeping with joy, and said, ‘O Messenger of Allaah (S), good news! Allaah 
    has answered your prayer and guided the mother of Abu Hurayrah.’ He praised and thanked Allaah.” 
(Narrated by Muslim, 2491)
And Allaah knows best.