Is there sin upon the mother and the son due to the failure to include the deceased grandfather, who passed away a year after the father, in the legal inheritance distribution document (Qassam Shar'i)?

Your grandfather is among the heirs as long as he was alive at the time of his son's death. If the division that took place did not account for his share, then it is incorrect. There is no sin upon you if you previously notified them of his existence, but the competent authorities must be consulted to correct the division and pay his share to his heirs. Alternatively, you yourselves must return his share to his heirs from what you took from the inheritance, because his right does not lapse by death, statute of limitations, or an incorrect division, nor does it justify your taking his share. The competent authority must correct the error.