Is it obligatory to confront a female relative who stole a ring from the questioner's house, despite the absence of current proof, knowing that she admitted to a previous theft from the mother's house? And is cutting ties with her considered a severance of kinship? And is it permissible for the questioner to suspect her without proof after all that has been mentioned?

Harming Muslims is forbidden. However, if you are certain your relative stole, confront her privately and offer her concealment in exchange for returning the ring. Threaten to expose her or report the matter to authorities if she does not comply. If that does not work, then there is no harm in cutting ties with her to deter her or for fear of being influenced by her, as severing kinship ties is a grave matter in the sight of Allah.