Is there any sin upon a mother for letting her daughter sleep with the one-day-old infant, knowing that the mother is elderly?

If both a cause and a direct actor are involved, liability falls upon the direct actor. Therefore, the blood money is incumbent upon your cousin, who was the direct cause of the killing, and expiation is also incumbent upon her. As for the blood money for accidental killing, it is borne by the 'aqilah (the male agnatic relatives).