Are we considered disobedient to our grandmother and sinful if she dies while angry with us due to our aunt's slanders, even though we are innocent of them?

Your aunt, while excelling in righteousness towards her parents, is errant in severing ties of kinship and harming you. You have acted rightly in striving to reconcile with her. We advise you to supplicate for her, asking Allah to rectify her situation, and to engage someone who holds influence with her to advise her gently. You will not be considered disobedient to your grandmother unless you have caused her harm. Your aunt's mere accusations do not make you disobedient. The forbidden disobedience (aqooq) is every action that causes a parent significant harm, unless the action is obligatory or involves polytheism or disobedience (to Allah). Your grandmother should be advised to verify information, in accordance with the verse: (O YOU WHO HAVE BELIEVED, IF THERE COMES TO YOU A DISOBEDIENT ONE WITH INFORMATION, INVESTIGATE). The supplication of the oppressed is answered. Continue to supplicate for her, not against her. You may boycott her if the boycott benefits her, otherwise, do not, for a boycott may increase stubbornness. There is no harm in supplicating that Allah reveal your innocence from what she attributes to you.