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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If the reasons and conditions of inheritance are met and there are no impediments then one has the right of inheritance whether he is sane or insane, pubescent or minor. The same is true in the case of the testator. Inheritance does not depend on mental ability. Hence this (insane) girl inherits from her mother just like her other normal sisters.
Therefore, if there is no other inheritors except those who have been mentioned in the question than all the belongings of the dead woman are distributed among her children; with the male getting twice the share of the female. Allaah says (interpretation of meaning): {Allah instructs you concerning your children [i.e. their portions of inheritance]: for the male, what is equal to the share of two females.}[4:11].
Finally, we advise you to consult any Islaamic center in your area to make sure that there are no other relatives who deserve inheritance except those who were mentioned in the question, and also there are no debts or a will which need to be settled before distribution of the inheritance among the heirs.
Allaah knows best.