Her husband does not want more children but she does
Question

                Allah has blessed us with 2 beautiful and healthy children. My husband is of the opinion that in this day and age it's enough. He does not want more kids. If I talk to him and tell him that I would like to have another baby, he sometimes gets angry or tells me he will get a vasectomy. I do not want him to do haram, but I long to have another child, in sha Allah. Can I refuse to have intercourse with him, when he is using protection or am I not allowed to? If he is not changing his mind, am I allowed to ask him for divorce? Or is it better to stay with him for the sake of the children and put my desires last?.
Praise be to Allah.
    Firstly: 

    Having a lot of children is something that is encouraged in 
    Islam and the Prophet (blessings and peace of Allah be upon him) urged 
    Muslims to do that. Abu Dawood (2050) narrated that Ma’qil ibn Yasar (may 
    Allah be pleased with him) said: A man came to the Messenger of Allah 
    (peace and blessings of Allah be upon him) and said: “O Messenger of 
    Allah, I have found a woman who is from a good family and is beautiful, but 
    she does not bear children; should I marry her?” He told him not to. Then he 
    came to him a second time and said something similar and he told him not to 
    marry her. Then he came to him a third time and said something similar and 
    he (peace and blessings of Allah be upon him) said: “Marry the one who is 
    loving and fertile, for I will be proud of your great numbers.” 

    Classed as saheeh by al-Albani in Irwa’ al-Ghaleel, 
    1784. 

    Hence the couple should be keen to have a lot of children and 
    be happy about that and show gratitude for the blessing that Allah has 
    bestowed upon them. 

    Secondly: 

    It is permissible to delay having children for a certain 
    amount of time if that serves an interest, such as if the woman is weak or 
    sick. But it is not permissible to do that for fear of poverty or for fear 
    of raising the children, because that implies thinking negatively of Allah, 
    may He be exalted. 

    It says in a statement of the Islamic Fiqh Council belonging 
    to the Muslim World League: The Islamic Fiqh Council affirms unanimously 
    that it is not permissible to limit the number of children in general and it 
    is not permissible to prevent pregnancy if the reason for doing that is fear 
    of poverty, because Allah is the Provider and Owner of great power, and 
    there is no living creature on earth but its provision is due from Allah, or 
    if that is for other reasons that are not acceptable according to 
    sharee’ah. 

    As for using means of preventing or delaying pregnancy in 
    individual cases where real and certain harm will result from it, such 
    as if the pregnant woman will have to give birth in a manner other than that 
    which is usual, and she will have to have surgery to bring the child forth, 
    in which case there is nothing in sharee’ah to prevent her doing that. The 
    same applies if it is delayed for other legitimate shar’i or health reasons 
    confirmed by a trustworthy Muslim doctor. Contraception becomes a must in a 
    case where it is proven that harm would result for the mother or there is 
    the fear that she may die, according to the opinion of a trustworthy Muslim 
    doctor. End quote from Fatawa Islamiyyah, 3/200. 

    Ash-Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was 
    asked: Is it permissible to use birth control so that a person has a child 
    every five years, because he sees the corruption in society and would not be 
    able to raise a lot of children close in age in this overwhelmingly corrupt 
    society? 

    He replied: So long as this is the intention, then it is not 
    permissible to do this, because it reflects a lack of trust in Allah with 
    regard to the hadeeth of the Prophet (peace and blessings of Allah be upon 
    him) who said “Marry the one who is loving and fertile…” 

    But if the birth control has to do with the condition of the 
    woman – because she cannot cope with repeated pregnancies – this may be 
    permissible, but it is better not to do it.

    End quote. Please see the answer to question number
    7205. 

    Thirdly: 

    It is permissible to use condoms and withdrawal, i.e., 
    ejaculating outside the vagina, on condition that you ask your wife's 
    permission to do that, because she has the right to pleasure and to have a 
    child. 

    The evidence that withdrawal is permissible is the hadeeth of 
    Jabir ibn ‘Abd-Allah who said: We used to engage in ‘azl at the time of 
    the Messenger of Allah (blessings and peace of Allah be upon him). News of 
    that reached the Messenger of Allah (and peace of Allah be upon him) and he 
    did not forbid us to do it.

    Narrated by al-Bukhari (5209) and Muslim (1440). 

    The husband does not have the right to do that without the 
    consent of his wife, because of what has been stated above. 

    If he insists on his attitude even though you want a child, 
    then he is doing wrong, but you should not respond to his action by refusing 
    to share his bed, because two wrongs do not make a right. Al-Bukhari (3237) 
    and Muslim (1736) narrated that Abu Hurayrah (may Allah be pleased with 
    him) said: “The Messenger of Allah (peace and blessings of Allah be upon 
    him) said: ‘When a man calls his wife to his bed and she refuses, and he 
    went to sleep angry with her, the angels will curse her until morning.’” 

    So do your duty and ask Allah for your rights. Be patient and 
    seek reward with Allah, and continue to advise him and do not ask for 
    divorce. Rather you should protect your home and your family, and pay 
    attention to raising your children. Ask Allah for righteous offspring, for 
    if it is decreed that a child should be born, that will not be prevented by 
    withdrawal, condoms or anything else. 

    Ahmad narrated from Jabir with regard to withdrawal that he 
    said: I used to withdraw from her -- meaning the slave woman – and have 
    intercourse with her, and she bore a child. The Messenger of Allah (blessings 
    and peace of Allah be upon him) said: “If Allah decrees that a soul should 
    be created, then it will come into existence.” 

    And al-Bukhari (5210) and Muslim (1438) narrated that 
    Abu Sa’eed al-Khudri said: We captured some female prisoners and we engaged 
    in coitus interruptus, then we asked the Messenger of Allah (blessings and 
    peace of Allah be upon him) about that and he said to us: “Do you do that? 
    Do you do that? Do you do that? There is no soul that is to exist, until the 
    Day of Resurrection, but it will come into being.” 

    May Allah help us all to do that which He loves and which pleases Him. 

    And Allah knows best.