Who Are Ahl al-Bayt?
Question

Who are Ahl al-bayt? Hadith Al-thaqalayn stated that Fatimah, Ali, al-Hasan & and al-Husain are among ahl bayt ar-rasul (members of the Prophet’s family)?
Praise be to Allah.Who are Ahl al-Bayt?
There are several views among the scholars (may Allah have mercy on them) concerning the definition of Ahl al-Bayt . Some said that the members of the Prophet’s family are his wives, his children, Banu Hashim, Banu al-Muttalib and their freed slaves. 
Some said that his wives were not part of the Ahl al-Bayt. Some said that the Ahl al-Bayt are Quraysh; some said that the family of Muhammad are the pious among his ummah; and some said that they are all of the ummah of Muhammad (peace and blessings of Allah be upon him).
Are the Prophet’s wives from Ahl Al-Bayt?
With regard to the wives of the Prophet (peace and blessings of Allah be upon him), the most correct view is that they are included among the members of the family of the Prophet (peace and blessings of Allah be upon him), because Allah says, after commanding the wives of the Prophet (peace and blessings of Allah be upon him) to observe hijab (interpretation of the meaning):
“Allah wishes only to remove Ar-Rijs (evil deeds and sins) from you, O members of the family (of the Prophet), and to purify you with a thorough purification” [al-Ahzab 33:33]
  And the angels said to Sarah the wife of Ibrahim (peace be upon him) (interpretation of the meaning):
“The Mercy of Allah and His Blessings be on you, O the family [of Ibrahim (Abraham)]” [Hood 11:73]
And because Allah excluded the wife of Lut from the family of Lut (peace be upon him) with regard to survival, when He said (interpretation of the meaning):
“(All) except the family of Lut. Them all we are surely going to save (from destruction). Except his wife…” [al-Hijr  15:59-60]
This indicates that the wife is part of the family.
Is the family of ‘Abd al-Muttalib from Ahl al-Bayt?
With regard to the family of al-Muttalib, it was stated in a report from Imam Ahmad that they are among them [among the Ahl al-Bayt]. This is also the view of Imam al-Shafi'i. Imam Abu Hanifah and Imam Malik were of the view that the family of Muttalib are not included in the family of the Prophet (peace and blessings of Allah be upon him); there is also a report to this effect from Ahmad. 
The correct view is that Banu ‘Abd al-Muttalib are among the Ahl al-Bayt . The evidence for that is the report narrated from Jubayr ibn Mut’im (may Allah be pleased with him) who said: “ ‘Uthman ibn ‘Affan and I went to the Messenger of Allah (peace and blessings of Allah be upon him) and said: ‘O Messenger of Allah, you have given to Banu’l-Muttalib and not to us, but we and they are the same in status with regard to you.’ The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘Banu’l-Muttalib and Banu Hashim are the same thing.’” (Narrated by al-Bukhari, no. 2907; al-Nasaa’i, 4067; and others)
Are Banu Hashim ibn ‘Abd Manaf among Ahl al-Bayt?
Included among the Ahl al-Bayt are Banu Hashim ibn ‘Abd Manaf, who are the family of ‘Ali, the family of ‘Abbas, the family of Ja’far, the family of ‘Aqil and the family of al-Harith ibn ‘Abd al-Muttalib. 
This was stated in the report narrated by Imam Ahmad from Zayd ibn Arqam (may Allah be pleased with him), in which he said: “The Messenger of Allah (peace and blessings of Allah be upon him) stood up and addressed us one day at a well called Khum, between Makkah and Madinah. He praised Allah and exhorted and reminded us. Then he said: ‘O people, I am a human being; soon the messenger of my Lord [i.e., the Angel of death] will come to me and I will answer his call. I am leaving among you two important things: the first of which is the Book of Allah, in which there is guidance and light, so adhere to it and follow it’ – and he urged us to adhere to the Book of Allah, then he said: ‘And the people of my household (ahl bayti). I remind you of Allah with regard to the people of my household, I remind you of Allah with regard to the people of my household, I remind you of Allah with regard to the people of my household.’” Husayn said to him [Zayd], “Who are the people of his household, O Zayd? Are not his wives among the people of his household?” Zayd said: “His wives are among the people of his household, but the people of his household are those who are forbidden to receive sadaqah (charity) after his death.” He (Husayn) said: “Who are they?” He said: “They are the family of ‘Ali, the family of ‘Aqil, the family of Ja’far and the family of ‘Abbas.” Husayn said: “Are all of these forbidden to receive sadaqah?” Zayd said, “Yes.” (Narrated by Ahmad, no. 18464)
Are the freed slaves of the Prophet among Ahl al-Bayt?
With regard to the freed slaves, it was narrated that Mihran the freed slave of the Prophet (peace and blessings of Allah be upon him) said: the Messenger of Allah (peace and blessings of Allaah be upon him) said; “We are the family of Muhammad: the sadaqah is not permissible for us, and the freed slave of a people is one of them.” (Narrated by Ahmad, no. 15152)
So the family of the Prophet (peace and blessings of Allah be upon him) are: his wives, his children, and Banu Hashim, Banu ‘Abd al-Muttalib and their freed slaves. 
For Issues related to Ahl al-Bayt, please see these answers: 146369 , and 112754 .
And Allah knows best.