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.
Since the deceased has debts, it is obligatory to repay them from his estate before dividing it among his heirs because debts take priority over the right of the heirs in the inheritance, as Allaah Says (what means): {…after any bequest he [may have] made or debt.}[Quran 4:11]
The Fiqh Encyclopedia reads: “It is not permissible for the heirs to divide the estate as long as the deceased has debts to be paid off, because it is only after the repayment of the deceased’s debts that the shares of inheritance can be evidently known and possessed by the heirs as Allaah Says (what means): {…after any bequest he [may have] made or debt.}[Quran 4:11] In case they divide it before the repayment of the debts, then their division is cancelled so as to preserve the rights of the creditors, because they (the heirs) have divided what they have not yet possessed.” [End of quote]
After the repayment of the debts, the inheritance is to be divided according to Sharee'ah.
Therefore, if the deceased did not leave any other heirs except those mentioned in the question, then his mother gets one-sixth as her prescribed 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] His wife gets one-eighth as her prescribed share due to the existence of the children (direct heirs); Allaah Says (what means): {...But if you leave a child, then for them [i.e. the wives] is an eighth of what you leave, after any bequest you [may have] made or debt...}[Quran 4:12]
His four daughters get two-thirds as their prescribed share which they would divide between themselves equally, as Allah Says regarding a group of daughters (what means): {...But if there are [only] daughters, two or more, for them is two thirds of one’s estate...}[Quran 4:11]
The remainder should be divided equally among the two full-sisters 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 it was authentically reported that the Prophet gave the sister the remainder of the inheritance after the share of the daughter and the son's daughter. The Hadeeth was related by Huzayl ibn Shurahbeel and reported by Al-Bukhari. It is for this reason that the scholars considered the sister as an heir via Ta'seeb with the daughters and the son's daughters, as she (the sister) takes whatever remains of their (daughters and sons' daughters') shares of inheritance.
Therefore, the inheritance should be divided into 48 shares: the mother of the deceased gets one-sixth, which is 8 shares; the wife gets one-eighth, which is 6 shares; and the daughters get two-thirds, which is 32 shares, and each of them gets 8 shares. The remainder is 2 shares which should be divided between the two full-sisters by way of Ta’seeb. Each of them gets 1 share.
As regards what you mentioned that most of the inheritance is earned from the work of the wife and that she owns it, then the answer is that what was registered under the name of the husband from the inheritance and was under his control and disposition during his life, then, in principle, it is his property and not the wife’s. Hence, if the wife claims that it is her property, and the heirs did not hold her to be truthful in this claim, then she may be requested to establish Bayyinah (legal proof) in support of her claim. If she does so, she is entitled to what she claims to possess, and if she does not, then the heirs are requested to swear (make an oath) that they do not affirm that she possesses what she claims to possess. If they refuse to swear, then she swears and takes what she claims. But if they swear, then she is not entitled to anything. The same applies if she refuses to swear after they have refused to swear [i.e., then she is not entitled to anything].
Of course, all of this should take place at an Islamic court or under the supervision of a scholar who is eligible to pass judgments if there is no Islamic court.
With regard to what was registered in the name of the wife or which was under her disposal and possession and she claims that it is her property, then in principle it is her property, so she is not required to establish proof for it. If the heirs claim that it is the property of the husband, then it is they who are required to provide evidence according to what we have mentioned above.
This is because if someone has something in one's immediate possession and disposes of that thing as its owner, then this serves as preponderant evidence that he is its owner.
The Fiqh Encyclopedia reads: “There is no disagreement among the jurists that physical possession in a disputed matter is one of the reasons that one's claim of ownership is preponderant if there is no stronger evidence such as Bayyinah (legal proof). Thus if two people dispute over the ownership of something which is physically possessed by one of them, and none of them has evidence to prove his claim, then it is ruled that it belongs to the one who has physical, or actual, possession of it according to the agreement of the jurists. This is based on the report which reads “The Bayyinah (establishing proof) is due upon the claimant and the oath is due upon the one who denies.” [End of quote]
The jurists have elaborated in the books of Fiqh on the issue of dispute on the ownership of something and to whom it should belong, so we are not going to elaborate more on this; rather, when there is a dispute, one has to resort to an Islamic court as we have mentioned when there is a conflict between the heirs, or to someone who may act instead of the Muslim judge when there is no Islamic court.
Allaah Knows best.