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 debts for which the deceased is liable must be paid before his estate is divided among the eligible heirs. The expenses of performing Hajj should also be deducted from the estate; this is because the settlement of the debts and liabilities are given precedence over the eligible heirs’ right to the deceased’s estate.
Scholars held different opinions regarding which debt should be given priority: that owed to Allaah (expense of Hajj and the like) or owed to people (debts) if the estate is not sufficient to cover both debt owed to Allaah and debt owed to people. Al-Mawsoo‘ah Al-Fiqhiyyah (Encyclopedia of Jurisprudence) reads: "If the estate is not sufficient to cover both, the Hanafi jurists held that the debts owed to Allaah are waived with death unless the deceased stated their repayment in his will as will be clarified later. The Maaliki jurists held that the payment of debts owed to people should be given priority over those owed to Allaah because the rights due to Allaah are subject to His forgiveness, whereas the right of a human must be fulfilled, unless one (its owner) relinquishes it; or because Allaah is not in need of anything while people are in need of their rights. The Shaafi‘i jurists held that the rights of Allaah take precedence over the rights due to humans if the estate is not sufficient to repay both. They relied on the following Ahaadeeth: The Prophet, sallallaahu ‘alayhi wa sallam, said: “The debt of Allaah has more right to be fulfilled.” He, sallallaahu ‘alayhi wa sallam, also said: “Fulfill the rights of Allaah, for He has more right to fulfillment.”
Ibn ‘Uthaymeen said: “Some scholars held that both are to be repaid proportionally (i.e. a share should be deducted for the repayment of the debts owed to Allaah and another to repay the debts owed to people). They both should be repaid because both constitute debts for which the deceased is liable; none of them should be given priority over the other. This is the opinion held by the Hanbali jurists and this is the preferred opinion in this regard.” [Sharh Az-Zaad]
It should be noted that the opinion of the Maaliki scholars cited in Al-Mawsoo‘ah Al-Fiqhiyyah does not apply to Hajj, as they hold that it is invalid to perform (the obligatory) Hajj on behalf of the deceased unless he stated it in his will even if he was not liable for any other debts.
If the deceased did not leave any eligible heirs besides those mentioned in the question, then each of the deceased’s mother and father get one-sixth of the estate as a fixed share because the deceased has children; Allaah, The Exalted, says (what means): {And for one's parents, to each one of them is a sixth of his estate if he left children} [Quran 4:11]
The residue of the estate should be divided among the two sons and daughter by Ta‘seeb (i.e. by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares are distributed); the male gets double the share of the female. Allaah, The Exalted, says (what means): {Allaah instructs you concerning your children: for the male, what is equal to the share of two females.} [Quran 4:11]
The grandson, the full brother, and the unborn full sibling are entirely excluded from inheritance by the presence of the two sons.
Hence, the estate should be divided into thirty shares; the mother gets one-sixth of the estate (five shares), the father gets one-sixth (five shares), each son gets eights shares and the daughter gets four shares.
Allaah Knows best.