Can the mother ask the father for payment in return for breastfeeding her children from him?
Question

Does the wife have the right to financial compensation from the husband if she breastfeeds his children?.
Praise be to Allah.Some scholars are of the view that if the wife asks her husband for payment for breastfeeding her children from him, then he must pay her, and they quoted as evidence the verse in which Allah says (interpretation of the meaning): “Then if they give suck to the children for you, give them their due payment” [al-Talaaq 65:6]. 
This is the view of Imam Ahmad (may Allah have mercy on him). 
See: al-Mughni, 11/431. 
But the correct view concerning this matter is that if the wife is married to the husband, it is not permissible for her to ask for payment in return for breastfeeding their children, because this is a duty on her and in that case she is not entitled to anything more than maintenance, because Allah says (interpretation of the meaning): “The mothers shall give suck to their children for two whole years, (that is) for those (parents) who desire to complete the term of suckling, but the father of the child shall bear the cost of the mother’s food and clothing on a reasonable basis” [al-Baqarah 2:233]. 
But if she is divorced and is no longer married to her husband, then she may ask for payments in return for breastfeeding her children from him, because Allah says (interpretation of the meaning): “Then if they give suck to the children for you, give them their due payment” [al-Talaaq 65:6]. This verse refers to one who is divorced, whereas the first verse refers to one who is still married. 
This is the view of Imam Abu Haneefah (may Allah have mercy on him) and is the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him). Among contemporary scholars it is regarded as more correct by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him). 
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 
Breastfeeding a child is obligatory for the mother, on condition that she be with her husband. This is the view of Ibn Abi Layla and others among the earlier generation, and she is not entitled to any payment in addition to her maintenance and clothing. This is the preferred of view of al-Qaadi and is the opinion of the Hanafis, because Allah says (interpretation of the meaning): “The mothers shall give suck to their children for two whole years, (that is) for those (parents) who desire to complete the term of suckling, but the father of the child shall bear the cost of the mother’s food and clothing on a reasonable basis” [al-Baqarah 2:233]. In this verse we see that what enjoined for them is clothing and maintenance on a reasonable basis. This is what she is entitled to as a wife, and it may be that to this may be added what is needed by a breastfeeding woman as Allah says concerning one who is pregnant (interpretation of the meaning): “And if they are pregnant, then spend on them till they lay down their burden” [al-Talaaq 65:6]. So the spending on the child is included in the spending on his mother, because he is nourished by what she eats. The same is true in the case of breastfeeding. In this case maintenance is obligatory for two reasons, so that if the duty is waived for one reason, it is confirmed for the other. So if a wife is wilfully defiant but is breastfeeding her child, she is entitled to maintenance because of breastfeeding, not because of being a wife. As for the one who is irrevocably divorced from the husband but is breastfeeding a child of his, she is undoubtedly entitled to payment, as Allah says (interpretation of the meaning): “Then if they give suck to the children for you, give them their due payment” [al-Talaaq 65:6]. End quote. 
Al-Ikhtiyaaraat, p. 412, 413. 
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 
The apparent meaning of the author's words is that the payment should be given to her whether the mother is with him or is irrevocably divorced from him. If the mother asks her husband to pay her for breastfeeding the child, if she is married to him, then he must give her the payment. We understand this from the words of the author, “and the father must arrange for his child to be breastfed.” And he did not limit it to cases where the mother is irrevocably divorced. The evidence for that is the general meaning of the words of Allah (interpretation of the meaning): “Then if they give suck to the children for you, give them their due payment” [al-Talaaq 65:6]. This view of the author is well known view in the madhhab [i.e., the madhhab of Imam Ahmad], and the payment is her right. 
Shaykh al-Islam favoured the view that if the woman is still married to the husband, she is not entitled to anything except maintenance only, and she does not have the right to ask for payment. What the Shaykh said is more correct, because Allah says (interpretation of the meaning): “Then if they give suck to the children for you, give them their due payment” [al-Talaaq 65:6], but this applies to divorced women, and a divorced woman is not with the husband. As for the woman who is with her husband, Allah says (interpretation of the meaning): “The mothers shall give suck to their children for two whole years, (that is) for those (parents) who desire to complete the term of suckling, but the father of the child shall bear the cost of the mother’s food and clothing on a reasonable basis” [al-Baqarah 2:233]. If you say: If she is a wife, then the husband is obliged to provide maintenance and clothing as a duty towards his wife, whether she breastfeeds or not, we say: There is no reason why there should not be two reasons for spending, then if one of them ceases to apply the other will remain. If the wife in this case is wilfully defiant, she is not entitled to maintenance on the basis of being a wife, but on the basis of breastfeeding she is entitled to maintenance. It is well known that if you study the situation of people at the time of the Messenger (blessings and peace of Allah be upon him) and until the present day, you will not find any woman who asked her husband for payment for breastfeeding a child. And this is the correct opinion. End quote. 
Al-Sharh al-Mumti’, 13/515, 516 
And Allah knows best.