All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The two sons of your sister are not heirs, just as your two sons are also not heirs. Your father’s bequest to the sons of your sister is a bequest for those who are not heirs, so it is valid and is taken from the third of the estate. However, his bequest for them, excluding your sons, is a controversial issue among the scholars regarding equal treatment of one’s grandchildren. Some said that equal treatment is a must and others said it is not. Tufhat al-Muhtaaj (by Al-Haytami) reads: "It is prescribed for the father, i.e. the progenitor, no matter how far up he is, to be fair in giving to his children, i.e. the progeny, no matter how far down they are — even while direct children exist, so that some do not receive more or less than the others, according to the soundest opinion. This is in accordance with the opinion of many jurists, and contrary to the opinion of those who made this ruling peculiar to the direct children. This is regardless of whether the thing given was a grant or a gift or charity or endowment or a donation. If he is not fair without a valid excuse, then it is disliked according to most of the scholars. Some have even said it is prohibited."
The opinion of the Hanbali School of jurisprudence is that equality between grandchildren is obligatory, just as it is between direct children. Al-Mardaawi said in Al-Insaaf, commenting on Al-Muqni‘ by Ibn Qudaamah: "His saying: "regarding gifts to children" includes the children of one’s children; this is indicated by his following statement: "the division among them is according to their share in the inheritance". There could be an heir from among the children of a child, and this is the main opinion apparently professed by our companions in the (Hanbali) Math-hab....."
Thus, you can see that this matter is a controversial issue among the scholars, but the opinion we adopt here in our site is the absence of such an obligation for equality between grandchildren. Based on that, your father’s bequest to some of his grandchildren and not others is a valid bequest, and it proceeds within the boundaries of the one third of the estate. For more benefit, please refer to Fatwa 2331.
Moreover, you should take note that what your father wrote for you and others of his heirs is considered a “bequest for an heir”; and it is prohibited by Islamic law, due to the Hadeeth of Abu Umaamah Al-Baahili who said: I heard the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, saying: “Verily Allaah has given every rightful person his right, so there is no bequest for an heir.” This was related by Ahmad, Abu Daawood, Ibn Maajah, and At-Tirmithi. Ahmad and At-Tirmithi deemed it Hasan (good). Ibn Khuzaymah and Ibn al-Jaarood deemed it strong (authentic). Ad-Daaraqutni narrated it through the Hadeeth of Ibn ‘Abbaas but added at the end of it: “Unless the heirs so will”, i.e. unless they all agree to it. Ibn Hajar considered its Isnaad (chain of narrators) to be Hasan (good).
To sum up, this document is not a binding bequest, rather its fulfillment is based on the approval of the other remaining heirs. If they are content with it, it is fulfilled. If they are not content to process it, then whatever your father wrote on your names should be included in the inheritance and be divided according the Islamic way of distributing the inheritance.
For more benefit, please refer to Fatwa 196061.
Allaah Knows best.