She became Muslim but her husband did not; is it allowed for her not to stop living with him because of his poor health and her financial situation?
Question

                I have been a Muslimah for the past 6 years, alhamdulillah. I came to Islam after almost 20 years of marriage. My son who is 11 years old is also a Muslim. I am bringing him up under the teachings of Islam. However, his father is not a Muslim and I know that according to Shariah Law my marriege was broken from the moment that I took my shahadah. HIs father does not practice any religion and he does not want to learn about Islam. We still live in the same house but we stopped sharing the same bed for a long time.We dont have intimacy at all. My son's father is also a disable due a car accident years back. We share the same house but I deal with him more as a caregiver. I think many times about living this house so I could have more freedom to practice my religion,including wearing the hijab when I go out with him, but I don't have the courage to leave him because of his condition and I also can't support myself. My parents are poor and I don't have much education and I also worry about my son.
Please send me an advice concerning this situation and tell me if is a major sin for me not to go out with a hijab with my husband when he forced me not to do it. I wear the full hijab all the time when I am alone, but once I stepped out of the house with him, he tells me to removed it.
Praise be to Allah.
      We praise Allah for having blessed you with Islam, and we 
      ask Him to make us and you steadfast in adhering to His true religion. 

    If a woman becomes Muslim and her husband refuses to become 
    Muslim, she is not permissible for him because Allah says (interpretation of 
    the meaning):

    “then if you ascertain that they are true believers send 
    them not back to the disbelievers. They are not lawful (wives) for the 
    disbelievers nor are the disbelievers lawful (husbands) for them”

    [al-Mumtahanah 60:10]. 

    Al-Shawkaani (may Allah have mercy on him) said: 

    The words of Allah, “They are not lawful (wives) for the 
    disbelievers nor are the disbelievers lawful (husbands) for them” 
    explain the reason why it is forbidden to send them back. This indicates 
    that a believing woman is not permissible for a kaafir and that if the woman 
    becomes Muslim she must leave her husband. End quote. 

    Fath al-Qadeer, 5/301 

    So it is not permissible for a Muslim woman to remain married 
    to a kaafir under any circumstances whatsoever. Rather they should be 
    separated as soon as she becomes Muslim, then she should wait until her 
    ‘iddah ends. If he becomes Muslim during the ‘iddah, that they remain 
    married, but if the ‘iddah ends and he has not become Muslim, she becomes 
    irrevocably divorced from him and she may marry someone else if she wishes, 
    or she may wait until he becomes Muslim. 

    Ibn al-Qayyim (may Allah have mercy on him) said: What is 
    indicated by the ruling of the Prophet (blessings and peace of Allah be upon 
    him) is that the marriage is suspended. If he becomes Muslim before the end 
    of her ‘iddah, then she is still his wife, but if her ‘iddah ends, then she 
    may marry whomever she wants, or if she likes she may wait for him, then if 
    he becomes Muslim, she is still his wife without any need for a new marriage 
    contract. End quote. 

    Zaad al-Ma‘aad, 5/137 

    As you say that you became Muslim six years ago, you became 
    irrevocably divorced from him a long time ago. So you have to leave him 
    immediately and it is not permissible for you to stay with him under any 
    circumstances. And you have to seek forgiveness and repent to Allah, may He 
    be exalted. 

    It is not permissible for you to serve him and take care of 
    him when Islam has separated you, especially since he -- in addition to 
    being a disbeliever -- hates religion and despises hijab and tells you to 
    take it off. How can you feel that you and your religious commitment are 
    safe when you are with him? 

    The Standing Committee for Issuing Fatwas was asked about a 
    Christian woman who was elderly, as was her husband. She became Muslim but 
    he did not, and there was no sexual relationship between them. Is it 
    permissible for her to stay with him or should the marriage be annulled? 

    They replied: 

    If a Christian woman becomes Muslim and she is the wife of a 
    Christian man, the marriage contract is annulled.  Based on that, it is not 
    permissible for her to stay with him even if they are old and have no sexual 
    relationship. End quote. 

    Fataawa al-Lajnah al-Daa’imah, 
    19/16-17 

    The fact that you are poor and have no work does not make it 
    permissible to you to stay in the same house as a non-Muslim man. Think 
    positively of Allah, may He be exalted, for He is the One Who says 
    (interpretation of the meaning):

    “Allaah will grant after hardship, ease”

    [al-Talaaq 65:7]. 

    Al-Sa‘di (may Allah have mercy on him) said: 

    This is glad tidings to those who are in difficulty, that 
    Allah will grant them relief from their hardship and take away their 
    difficulties. End quote. 

    Tafseer al-Sa‘di, p. 871 

    And Allah says (interpretation of the meaning):

    “And whosoever fears Allaah and keeps his duty to Him, He 
    will make a way for him to get out (from every difficulty).

    3. And He will provide him from (sources) he never could 
    imagine. And whosoever puts his trust in Allaah, then He will suffice him. 
    Verily, Allaah will accomplish his purpose. Indeed Allaah has set a measure 
    for all things”

    [al-Talaaq 65:2-3].

    Imam Ibn al-Qayyim (may Allah have mercy on him) debated with 
    a Christian scholar until the truth became clear to him, but he refrained 
    from entering Islam on the grounds that the Christians venerated him and he 
    said: I do not know any trade and I have not memorized any Qur’aan or 
    grammar or fiqh. If I become Muslim I will go around the marketplaces 
    begging from people. Who could agree to that? Ibn al-Qayyim said: That will 
    not happen! How can you think of Allah that if you give precedence to 
    pleasing Him over your whims and desires He would humiliate you and make you 
    in need of others? Even if we assume that that will befall you, what you 
    have attained of truth and salvation from the Fire and from the wrath and 
    anger of Allah will be the most complete compensation for what you have 
    lost. End quote. 

    Hidaayat al-Hayaara, p. 119 

    Your son should treat his father kindly and serve him and 
    help him as much as he can. That is his father’s right over him, even if he 
    (the father) continues to follow his present religion. Strive to call him to 
    Islam, for that will be better for both of you, so that the family will not 
    be divided. Tell him that Islam forbids you to stay with him, and that there 
    is no solution to this problem except his becoming Muslim. 

    We ask Allah to guide and help you all. 

    And Allah knows best.