Will a woman be rewarded for her work in the home even if she does not intend to seek reward?
Question

If a woman works in her house without intending to seek reward for her work with Allah, will she be rewarded for her work or not?.
Praise be to Allah.A woman’s work in the home is important work in which she helps to spread love and mercy in her home, and she plays a major role in raising her children and helps her husband in his work, da’wah and pursuit of knowledge. 
In this regard, this work is like all other kinds of work: a woman will not be rewarded for it unless her intention in doing it is sincerely for the sake of Allah alone. 
There follow some texts which support this view, as well as some of the comments of the scholars.
 1 – al-Bukhaari (may Allah have mercy on him) included in Kitaab al-Eemaan (the Book of Faith) a chapter in which he listed shar’i duties, which included seeking reward for doing them. 
Al-Bukhaari (may Allah have mercy on him) said:  
“Chapter: what was narrated about actions being but by intentions, and every person will have but that which he intended. This includes faith, wudoo’, prayer, zakaah, Hajj, fasting and other rulings. Allah says (interpretation of the meaning): “Each one does according to Shakilatihi (i.e. his way or his religion or his intentions)” [al-Isra’ 17:84]. A man may seek the reward of charity for his spending on his family. And the Prophet (peace and blessings of Allah be upon him) said: “But jihad and good intentions.” 
Saheeh al-Bukhaari (1/29), Kitaab al-Eemaan. 
Al-Haafiz ibn Hajar (may Allah have mercy on him) said:  
The words “Chapter: what has been narrated…” mean: a chapter which explains what has been narrated as evidence that shar’i actions are judged according to intention. 
Fath al-Baari (1/135, 136) 
2 – It was narrated that Abu Mas’ood al-Badri (may Allah be pleased with him) said: The Prophet (peace and blessings of Allah be upon him) said: “If a Muslim spends on his family, seeking reward for that with Allah, then it will an act of charity on his part.” Narrated by al-Bukhaari (55), Muslim (1002). 
Spending on his wife and children is a man’s shar’i duty, but he will not be rewarded for it unless he seeks reward thereby. 
Al-Qurtubi said: 
The apparent meaning is that the reward for spending on them can only be attained by intending to draw closer to Allah, whether it is obligatory or permissible, and this implies that whoever does not intend to draw closer to Allah will not be rewarded, but he has discharged his duty in the case of obligatory spending. 
Fath al-Baari (1/136) 
Ibn Hajar said: 
It may be understood from this that the reward cannot be attained by doing the deed unless it is also accompanied by the intention. 
Al-Tabari said: spending on one's family is obligatory, and he will be rewarded for what he gives according to his intention. There is no contradiction between its being obligatory and its being called charity, rather it is better than voluntary charity. 
Fath al-Baari (9/498) 
Al-Nawawi (may Allah have mercy on him) said: 
Seeking reward thereby means seeking the Countenance of Allah thereby. That does not include whatever he spends absent-mindedly (i.e., heedless of the intention and without intending to seek reward thereby). Rather this refers to the one who seeks reward. The way to seek reward is to spend it with the intention of fulfilling the duty of spending and kind treatment that has been enjoined upon him. 
Sharh Muslim (7/88, 89). 
3 – It was narrated from Sa’d ibn Abi Waqqaas (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “You will never spend anything, seeking thereby the Countenance of Allah, but you will be rewarded for it, even what you put in your wife’s mouth.” Narrated by al-Bukhaari (56) and Muslim (1628). 
Ibn al-Haaj al-Maaliki (may Allah have mercy on him) said: 
He should not neglect to give his wife a morsel or two, because the Prophet (peace and blessings of Allah be upon him) said: “even a morsel that he puts in his wife’s mouth.” He will earn reward even though there is some pleasure for him in putting a morsel in his wife’s mouth, but he should seek reward in all of that, i.e., in bringing the food and in giving it to her. 
Al-Madkhal (1/224). 
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 
You will never spend anything, seeking thereby the reward of Allah, but you will be rewarded for it. The attainment of reward is dependent upon that, i.e., on seeking the Countenance of Allah. This is what matters. 
Fath al-Baari (5/367). 
Conclusion: 
A woman will be rewarded for her work in the house if she seeks reward with Allah for that, and is sincere in her intention. 
And Allah knows best.