A Sunni view on the issue is that these are not accurate.
First, it is not established that the prophet gave Fadak to her.
Contrary to that there are hadith stating that she asked for it during the prophet's lifetime but the prophet refused her request. See e.g. [Sunnan Abi Dawood; Kitab Al-Kharaj, Wal-Fai' Wal-Imarah; hadith 2966].
Abu Bakr refused the inheritance argument by narrating from the prophet that
the inheritance does not apply to prophets property. See e.g. [Bukhari, Book 53, Volume 4, Hadith 325].
References:
And Allah knows best.
[Sunnan Abi Dawood; Kitab Al-Kharaj, Wal-Fai' Wal-Imarah; hadith 2966]:
[...]
Umar ibn Abdul-Aziz gathered the family of Marwan when he was made caliph and said:
"Fadak belonged to the Apostle of Allah (Peace Be Upon Him), and
he made contributions from it,
showing repeated kindness to the poor of the Banu Hashim from it, and
supplying from it the cost of marriage for those who were unmarried.
Fatima asked him to give it to her, but he refused.
That is how matters stood during the lifetime of the Apostle of Allah (Peace Be Upon Him) till he passed away.
When Abu Bakr was made ruler he administered it as the prophet (Peace Be Upon Him) had done in his lifetime till he passed on.
Then when Umar ibn al-Khattab was made ruler he administered it as they had done till he passed on.
Then it was given to Marwan as a fief, and it afterwards came to Umar ibn Abdul-Aziz.
I consider that
I have no right to something which the Apostle of Allah (Peace Be Upon Him) refused to Fatima, and
I call you to witness that I have restored it to its former condition;
meaning in the time of the Apostle of Allah (Peace Be Upon Him)."
[Bukhari, Book 53, Volume 4, Hadith 325]
Narrated Aisha:
Fatima sent somebody to Abu Bakr asking him to give her her inheritance from the Prophet
from what Allah had given to His Apostle through Fai
(i.e. booty gained without fighting).
She asked for the Sadaqa
(i.e. wealth assigned for charitable purposes) of the Prophet at Medina, and Fadak, and what remained of the Khumus (i.e. one-fifth) of the Khaibar booty.
Abu Bakr said:
Allah's Apostle said: "We (Prophets), our property is not inherited, and whatever we leave is Sadaqa, but Muhammad's(Sallalahu Alaihiwassalam) Family can eat from this property, i.e. Allah's property, but they have no right to take more than the food they need."
By Allah! I will not bring any change in dealing with the Sadaqa of the Prophet
(and will keep them) as they used to be observed in his life-time, and
I will dispose with it as Allah’s Apostle used to do."
Then Ali said:
"I testify that none has the right to be worshiped but Allah, and that Muhammad is His Apostle. O Abu Bakr! We acknowledge your superiority."
Then Ali mentioned their own relationship to Allah's Apostle and their right.
Abu Bakr then said: "By Allah in whose hands my life is. I love to do good to the relatives of Allah's Apostle rather than to my own relatives.
Look at Muhammad through his family
(i.e. if you are no good to his family you are not good to him)."
EDIT :
One simple comment to add here that the decision of Abu Bakr R.A. was right therefore Ali R.A in his Caliphate did not give Fadak to the children of Fatima R.A or took it for himself etc. If this was ever happened in the era of Ali R.A there would be a reference.
