Is it permissible for a woman to travel without a mahram for medical treatment if not traveling could lead to a hysterectomy, given that some of her children are minors and her adult son will take her to and pick her up from her destination? Is she sinful for doing so? And is the questioner sinful for not traveling with her as a mahram?

The journey of a woman with a teenage mahram (unmarriageable kin) is permissible according to the majority of scholars. Hanafi jurisprudence considers a teenager to be like an adult. The Maliki school stipulates discernment and sufficiency (in providing protection). The Shafi'i school permits a mahram to accompany a woman even if he is a teenager. Therefore, your aunt's journey with her son, who is nearing puberty, is permissible, and you incur no sin for not traveling with her. If your mother returns alone by plane on a safe journey, there is no objection to that.