Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In principle, the children whose mother died don`t inherit their grandfather. This is because there is no Sharia evidence stating as such. Moreover, they are maternal relatives and these don`t get to inherit as long as there is a relative from the `Asabat (Relatives in whose line of relationship no female enters) or Dhaw-u`l-Fara`id (Those who have right to definite shares in the assets left by the deceased). And Allah the Almighty Knows Best.