He died and left behind a wife, a mother, sons and daughters, and brothers and sisters. How should the estate be divided?

Firstly:

As there are children of the deceased, the brothers and sisters do not inherit anything, whether they were full siblings or siblings through the mother. 

Ibn Qudaamah said: A brother or sister through the father and mother, or through the father, do not inherit if there is a son or a son’s son, no matter how far the line of descent goes, or if there is a father. 

The scholars are unanimously agreed on this, praise be to Allah. End quote. Al-Mughni, 7/4. 

Ibn al-Mundhir said: And they were unanimously agreed that siblings through the mother do not inherit if there is a child, male or female. End quote. Al-Ijmaa’ by Ibn al-Mundhir, p. 18 

Based on that, the ones who inherit from this deceased are: the sons, the daughters, the wife and the mother only. 

The mother gets one-sixth, because Allaah says (interpretation of the meaning): “For parents, a sixth share of inheritance to each if the deceased left children” [al-Nisa’ 4:11]. 

The wife gets one-eighth, because Allah says (interpretation of the meaning): “In that which you leave, their (your wives) share is a fourth if you leave no child; but if you leave a child, they get an eighth of that which you leave” [al-Nisa’ 4:12]. 

What is left of the estate is to be divided among the children, with the male getting the share of two females, because Allah says (interpretation of the meaning): “Allaah commands you as regards your children’s (inheritance): to the male, a portion equal to that of two females” [al-Nisa’ 4:11]. So the remainder should be divided into nine parts, of which each son takes two and each daughter takes one. 

Secondly: 

After dividing the estate in the manner described above, the mother’s share, which is one-sixth, should be taken and distributed to her heirs who are, according to what is stated in the question, the brothers and sisters of the deceased who are her children. So it should be distributed among them with each male getting the share of two females. 

As for the share of the wife, it is one-eighth, so it should be distributed among her sons and daughters, with each male getting the share of two females, if she did not have any other heirs such as a father or mother. 

And Allah knows best.