Is a mother whose daughter died because she slept through her [needs] considered an accidental killer, and what is required of her to expiate her sin?

There is no blame on the mother, as you did not err in action or intent. The responsibility falls on your adult children if it is medically proven that their sister's death was due to sun exposure. In that case, they owe the expiation for accidental killing: freeing a slave. If they cannot find one, then fasting for two consecutive months. If their sister was an adult at the time of her negligence, then she owes the expiation for accidental killing. As for the blood money (diyah), it is a right for you and your husband, and you both have the right to waive it.