He set Fatima's house Ablaze after the death of the Prophet

Umar at Fatimah's house (in Arabic حرق الدار, means the burnt house) refers to the event where Umar came to the house of Fatimah, the daughter of the Islamic prophet Muhammad, in order to get the allegiance of Ali and his followers or burn her house down. This event is ascribed to be the cause of Fatimah's miscarriage and eventual her death.  Umar did not only threaten Fatima for burning her house rather he actually set it ablaze.

Some group of Muslim try to deny this incidence which has been cited by many ulama and historian. But what gult has Umar to set the house Fatima Zahra (a.s.) ablaze; was that not like setting the house of the holy Prophet (s.a.w.a.) ablaze? 

Remember that Fatima was the only surviving daughter of the Prophet as his entire children died in his life time. Does Fatima deserve to be treated as does by Umar?

Her house was burnt by Umar, her inheritance was usurped by Abu-Bakr, they caused the miscarriage of her son WHY? How will these people meet with the Prophet on the day of Judgment?

Historical fact and source about the setting ablaze the house of Fatima (a.s.)
Ibn Qutayba (276 AH/ 889 CE) in al-Imama wa al-Siyasa writes:
"Umar said: I swear by He who controls the life of Umar, either you come out or I will burn this house down! the people said: Abu Hafsa, Fatima is also in this house, Umar replied: even if she is....." 

{ibn Qutayba, al-Imama wa al-Siyasa (Egypt: Maktabt al- Tijaria al-Kubra}.

Al-Baladhuri (297 AH/ 892 CE) in Ansab al-Ashraf writes:
"Abu Bakr sent for Ali so that he can give alligance but he didn't. So Umar came [to the house] and Fatima met him at the door. She said: 'ibn Khatab you want to burn my door down?' Umar replied: 'Yes, in order to strengthen the religion your father brought.
{al-Baladhuri, Ansab al-Ashraf, vol. 1 (Cairo: Dar al-Ma'arif, 1959),}

The historian Muhammad ibn Jarir al-Tabari (923 CE) in his Tarikh writes:

"Umar Ibn al-Khattab came to the house of Ali. Talha and Zubayr and some of the immigrants were also in the house. Umar cried out: "By God, either you come out to render the oath of allegiance, or I will set the house on fire." al-Zubair came out with his sword drawn. As he stumbled (upon something), the sword fell from his hand so they jumped over him and seized him."
{The History of al-Tabari, Volume IX, The Last Years of the Prophet, p186-187, SUNY Press}

The book Ithbāt al-Waṣīyyah, composed in the third Islamic century, is attributed to the historian al-Mas’udi, The author writes:
"They attacked [Ali], burned his door and took him out by force and pressed [Fatima] against the door until she miscarried Muhsin."
He also writes:
While addressing the people Abu Bakr said: “…of the three mistakes that I committed, one of them is that during my time Fatima's house was broken into..”
{Tarikh al-Mas’udi, Volume 1-2, p 235-236, Nafees Academy, Karachi, Pakistan (Urdu Translation)}

Tarikh al-Ya’qoubi:
"..When Abu Bakr and Umar heard the news that a party of the Ansar and the Muhajirin have gathered with ‘Ali at the house of the daughter of the Prophet, they went with a group of people and attacked the house"
{Tarikh al-Ya’qoubi, Volume 2, p 199, Nafees Academy, Karachi, Pakistan (Urdu Translation)}.

With all these assertions do we still need to doubt weither Umar set the house of Fatima ablaze?