All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

 

Sons and daughters  of sons don`t inherit their grandfather while their paternal uncles are alive, and this is the reliable opinion of the four schools of Islamic thought (Maliki, Shafie`, Hanafi, and Hanabli). However, they do inherit according to the Personal Status Law effective in Jordanian courts nowadays based on Ijtihad (1) of some contemporary scholars. Consequently, any son of one`s son can take his share from their father`s share, even if the latter is alive, but of no more than 1/3rd. Nonetheless, it is better not to in order to be on the safe side as far as the rulings of Sharia are concerned.

As for the children of the sister who had passed away, they don`t get to inherit their deceased maternal uncle; neither according to the four schools of Islamic thought nor the Personal Status Law.

Accordingly, the wife gets 1/4th, the rest of the estate goes for the two full brothers, and the two living sisters get their share based on the rule "The male gets twice the share of the female." And Allah The Almighty Knows Best.

 

[1] Ijtihad (Arabic اجتهاد) is a technical term of Islamic law that describes the process of making a legal decision by independent interpretation of the legal sources, the Qur'an and the Sunnah. The opposite of ijtihad is taqlid, Arabic for "imitation." A person who applied ijtihad was called a mujtahid, and traditionally had to be a scholar of Islamic law or alim.