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 heirs must pay off the deceased’s debts first before the division of the estate because the payment of the debt is given priority over the rights of the heirs in the estate. After paying off the debts, the residue of the deceased’s estate should be divided among the eligible heirs as per the Sharee‘ah.
If the deceased did not leave heirs entitled to inherit other than those mentioned in the question, then the mother gets one-sixth of the estate and her father gets one-sixth as well as fixed shares because the deceased had 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 husband gets one-fourth of the estate as a fixed share because the deceased had children; Allaah, The Exalted, says (what means): {… But if they have a child, for you is one fourth of what they leave, after any bequest they [may have] made or debt…} [Quran 4:12]
The residue of the estate is to be divided among her two sons 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 have been distributed). The Prophet, sallallaahu ‘alayhi wa sallam, said: “Give the Faraa’idh (the shares of the inheritance prescribed in the Quran) to those who are entitled to receive them, and whatever is left should be given to the closest male relative of the deceased.” [Al-Bukhari and Muslim]
The deceased’s brother and sisters do not get any share because they are wholly excluded by the presence of the deceased’s sons or father. Ibn Al-Munthir wrote, “Scholars unanimously held that all brothers and sisters, both from the father’s and mother’s side, are totally excluded by the son and the son’s son or the father.” [Al-Ijmaa‘]
Hence, the estate should be divided into twenty four shares; the mother gets one sixth of them (four shares), the father gets one sixth as well (four shares), the husband gets one fourth of them (six shares), and each son gets five shares.
Allaah Knows best.