Is it forbidden for your aunt to have missed fasting and prayer—as a result of the excuse of her husband's and son's deaths—and what is the expiation for that?

Vowing is disliked. If a Muslim vows an act of obedience to Allah, he or she must fulfill it, for the Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him." If your aunt stopped fulfilling her vow due to an overwhelming excuse, there is no sin upon her, but she must make up the prayers and fasting. If there was no valid excuse, she must repent and make them up, and there is no expiation upon her.