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 is His slave and messenger.
If the deceased did not leave any other heirs except his mother and his two sons and the other heirs whom you have mentioned in the question, then his mother gets one-sixth as her legal share due to the existence of direct heirs (children) as Allaah 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 remainder should be divided equally among his two sons by Ta’seeb (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); as the Prophet said: "Give the prescribed share of inheritance to those who are eligible for it and the remainder [of it] is for the nearest male blood relative.” [Al-Bukhari and Muslim]
The other heirs whom you mentioned in the question do not get anything from the inheritance because they are prevented by the existence of sons.
Therefore, the inheritance should be divided into 12 shares: the mother of the deceased gets one-sixth, which is 2 shares, and each son gets 5 shares.
Allaah Knows best.