Am I obligated to pursue legal action to prove medical malpractice at the hospital and to punish the doctor who abandoned my mother during her acute asthma attack, and will I be punished if I do not demand blood money (diyya)?

May Allah grant you comfort in your bereavement for your mother. It is not permissible for you to hasten to accuse the doctor of negligence without clear proof. Rather, refer the matter to the responsible authorities for investigation. This matter has no relation to honoring one's mother, and refraining from it is not considered an act of disobedience. As for blood money (Diyya), it is a right belonging to the guardians of the slain, and they have the choice to demand it or to forgive it.