Is expiation (kaffarah) required for a deceased woman who did not observe the waiting period (iddat al-wafah) of four months and ten days after her husband abandoned her for thirty years, and her children took over the upbringing of their siblings?

Your grandmother was obligated to observe an 'iddah (definition) (waiting period) of four months and ten days after the death of her husband. Her husband's abandonment of her does not justify her abandoning the 'iddah, because it is an act of worship and obedience to Allah the Almighty. Allah says: "And those who are taken in death among you and leave wives behind - they, [the wives], shall wait four months and ten [days]." (Quran 2:234). As for now, there is nothing due from her heirs. However, they should frequently supplicate for her and give charity on her behalf, based on the Prophet's (peace be upon him) saying: "When a person dies, his deeds come to an end except for three: a continuous charity, knowledge from which benefit is derived, or a righteous child who prays for him."