Are grandchildren entitled to any share of their grandfather’s estate?
Question

If a daughter dies before her father, are her children entitled to any share of her father’s estate instead of her?.
Praise be to Allah.The grandchildren may be the children of a son or of a daughter. 
The children of a daughter do not inherit from their grandfather, whether their mother is alive or dead. 
The children of a son inherit from their grandfather so long as none of the grandfather’s children are alive, regardless of whether the son’s father or any of his paternal uncles are alive. If any of the grandfather’s own sons are alive, then the grandsons do not inherit, regardless of whether their father is alive or dead. 
See al-Tahqeeqaat al-Mardiyyah fi’l-Mabaahith al-Fardiyyah by Shaykh Saalih al-Fawzaan, p. 65, 125 
It is unknown in sharee’ah for a grandson to take the share of his deceased father, who would have taken it if he were alive.
 Rather the estate is to be shared out among the heirs who are alive at the time of their benefactor’s death. How can we give a share to this father who died before the grandfather, then take this share and give it to (the deceased father’s) children? Glory be to You (O Allah)! This is a great lie. 
These grandchildren who do not inherit from their grandfather because their grandfather’s own sons are still alive may get something from his estate in two ways: 
1 – If the grandfather left something to them in his will before he died, one-third or less of the estate. This applies if he has a great deal of wealth. Some scholars regarded such a will as binding or obligatory, others regarded it as mustahabb. 
The evidence for that is the verse in which Allah says (interpretation of the meaning): 
“It is prescribed for you, when death approaches any of you, if he leaves wealth, that he makes a bequest to parents and next of kin, according to reasonable manners. (This is) a duty upon Al-Muttaqoon (the pious)”
[al-Baqarah 2:180]
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Among the things we learn from this verse are: 
Bequests to parents and relatives of a man who leaves behind a lot of wealth must be fulfilled, because Allah says (interpretation of the meaning): “And it is prescribed for you”. The scholars differed as to whether this is abrogated by the verses on inheritance or is it is general and the verses on inheritance are specific? There are two views. The majority of scholars are of the view that it is abrogated, but the more correct view is that it is not abrogated, because it is possible to understand it as speaking in specific terms and say that the words “to parents and next of kin” apply if they are heirs, i.e., if they are heirs then no bequest can be made to them, and the shares of inheritance decreed by Allah are sufficient. So the general meaning of the verse still applies to those who are not heirs.
 Another lesson we learn is that it is permissible for a person to bequeath whatever he wants of his wealth, but this restricted by the hadeeth of Sa’d ibn Abi Waqqaas (may Allah be pleased with him) who said to the Prophet (peace and blessings of Allah be upon him): “Shall I give two-thirds of my wealth in charity?” He said, “No.” He said: “Then one half?” He said, “No.” He said: “Then one third?” He said: “One third, and one-third is too much.” Agreed upon. Based on this, the bequest should not amount to more than one third of the wealth, so the meaning of the verse is restricted by the hadeeth. 
The obligatory bequest is that which is left by one who has left behind a great deal of wealth, because Allah says: “if he leaves wealth” [al-Baqarah 2:190]. As for the one who leaves only a little wealth behind, it is better for him not to make any bequest if he has heirs, because the Prophet (peace and blessings of Allah be upon him) said to Sa’d ibn Abi Waqqaas (may Allah be pleased with him: “For you to leave your heirs independent of means is better than leaving them dependent and holding out their hands to people.” Agreed upon. 
Tafseer Soorat al-Baqarah, 2/306, 307 
2 – If their uncles give them some of their shares and distribute that among them. 
Calculating what would have been their father’s share and giving it to them when he is no longer alive is something for which there is no known basis in sharee'ah. In some states this is called the “binding bequest” and they give the children of the son who died during the lifetime of his father – i.e., their grandfather – the share that would have been their father’s, so long as it does not exceed one-third of the estate, and they give the children of a daughter the share that would have been their mother’s, so long as it does not exceed one-third, even if the grandfather did not bequeath anything to them. 
This is contrary to sharee’ah and does not have to be obeyed, because it is an attempt to share the role of Lawgiver with Allah and a transgression against the rights of the heirs. They attributed this idea to Ibn Hazm (may Allah have mercy on him), but it is a fabrication against him, because Ibn Hazm regarded it as obligatory to make bequests to relatives who do not inherit, which include the paternal uncle, maternal uncle and all other relatives, but they do not allocate a share of the estate to these relatives. Moreover, Ibn Hazm did not stipulate a specific amount or share, but they are doing that by giving the share of the father or mother. And Ibn Hazm said that they should be given something in cases where the grandfather has made a bequest, whereas they give these grandchildren a share even if the grandfather did not make any bequest. So what Ibn Hazm said is different from what they attributed to him. Judges should not issue such rulings, and they should realize that by issuing such rulings they are going against the law of Allah, may He be exalted, and taking wealth from those to whom Allah has given a right to it, and giving it to those who are not entitled to it. 
This is going against the ruling and laws of Allah. Many scholars of al-Azhar have objected to the “obligatory bequest law” and issued fatwas speaking against it. Papers have been published in the journal of al-Azhar refuting this law, and explaining how it goes against sharee’ah.  
Shaykh ‘Abd-Allah ibn Jibreen (may Allah have mercy on him) was asked: 
Can grandchildren inherit from their grandfather if their father died before their grandfather? If the answer is no, then why? 
He replied: 
Grandchildren refers to the sons of the son, not the sons of the daughter. If their father dies before his own father, they do not inherit from their grandfather if he has a son or sons of his own, because a son is a closer than a son’s son. If the grandfather does not have any other son but he has daughters, then the grandchildren inherit whatever is left after the daughters have been given their inheritance. Similarly, they inherit from their grandfather if he does not have any sons or daughters, so they take the place of his children, and each male is given the share of two females.   
Majallat al-Haras al-Watani, issue no. 264, dated 1/6/2004 
And Allah knows best.