Her husband does not pray and he refuses to divorce her until she gives him the child
Question

                My Sister married her hasband almost 5 years, and got one 3 years old daughter. Her husband also born muslim, but he doesn't follow the Islam rule. He not pray and fasting. She gave him time and try to told him with this issue. For the working also he was not working hard, just follow his feeling only. Sometimes he coudn't earn even cent for family. He is a lazy person. He depend much on my family especially my income, because we stayed together in one house. And now she escape away from her husband over 1 year already, and she asked the husband to divoice her, but he refused unless she gave the daughter to him. But as I told you above, he not a good man, and drink alcohol some more. Ths excused just he not want to divoice my sister only. Now my sister working in oversea and the daughter she brought back to keep with my mother to take care, untill he know that the daughter with my mother he never come to visit his daughter. In this case I want to ask you how to divoice with him, because he not agree to divoice my sister. When I asked the Islamic teacher in my village, he said cannot divoice him unless he agree to divoice my sister himself and try to teach him to parctise and follow the Islam. But we try our best for over than 3 years to encourage him to pray and to fast, but he not follow. So pls help us what can we do?.
Praise be to Allah.
    If the husband does not pray then it is not permissible for 
    your sister to stay with him, because the one who does not pray is a kaafir 
    according to the sounder of the two scholarly opinions. See the answer to 
    question no. 5208 and
    6257 

    If he did not pray during the marriage, then the marriage is 
    not valid but the child is to be attributed to him because she was born as 
    the result of a marriage which both partners thought was valid. 

    If he stopped praying after getting married and continued not 
    praying until her ‘iddah ended, then the marriage is annulled. But if he 
    repents and starts to pray, she can go back to him on the basis of a new 
    marriage contract if she agrees to. 

    Some of the scholars say: if he repents and starts to pray, 
    he may go back to her even if that is after the ‘iddah has ended, so long as 
    she has not got married to another husband. 

    From this you will know that according to sharee‘ah there is 
    no need for a divorce (talaaq) from him, but because she is regarded as his 
    wife in official papers and that has an impact on inheritance between them 
    and preventing her from marrying someone else, she has to try to get the 
    divorce even if she has to give him money so that he will divorce her. 

    With regard to the child, the mother is entitled to custody. 

    The husband should be advised to repent to Allah, may He be 
    exalted, and to pray. He should be told that his wife is not permissible for 
    him until he starts to pray. If he repents, praise be to Allah, but if he 
    remains as he is then your sister should try to get a divorce and she can 
    refer the matter to the court and ask for divorce because he is not spending 
    on her and because of the harm caused. 

    We ask Allah to grant her a way out.

     And Allah knows best.