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.
The children of the deceased woman are entitled to inherit from her, and the fact that they are not from the same father does not change anything in this regard because she is their mother. The male gets double the share of the female. If she has no other heirs entitled to inherit except her six sons and three daughters, then the estate should be divided among them by virtue of taʻseeb (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 male gets twice the share of the female; as Allaah, The Exalted, says (what means): {Allaah instructs you concerning your children: for the male, what is equal to the share of two females.} [Quran 4:11]
Hence, the estate should be divided into fifteen shares, each son gets two shares and each daughter gets one share.
Allaah knows best.