Is expiation (kaffarah) obligatory for a mother whose child, suffering from a rare disease, passed away, and she believes that her unintentional negligence in administering his medication was the cause of his death, despite doctors having informed her that his end was known since birth?

If the mother is certain, or it is highly probable in her estimation, that the child died due to not being given medicine, then she is obligated to offer expiation by fasting for two consecutive months. The blood money for the killing is paid by her 'Aqila (male relatives on the father's side) to the child's heirs, and the mother does not inherit anything from it. However, if these are merely doubts, then nothing is incumbent upon her.