How can one ignore his sister who interrupts and provokes him, and is it possible to deal with the feeling of hatred or her presumed mental illness?

To alleviate the situation and deal with your sister, it is advisable to counter ill-treatment with kindness, following the example of the Prophet (peace be upon him), as Allah the Almighty says: (Repel [evil] with that which is better) Fussilat/34. You must control your temper and not get angry for yourself; the Prophet (peace be upon him) only became angry when the limits of Allah were violated. Your sister is the most deserving of your dutifulness and bearing her ill-treatment, and true kinship is maintained with those who mistreat you. It should be remembered that being kind to your sister is an act of dutifulness to your parents, for the Prophet (peace be upon him) said: (Indeed, the most dutiful act of devotion is that a person maintains relations with the loved ones of his father) Narrated by Muslim. A Muslim should have a sound heart towards his siblings, and live with his sister with love and gentleness, openly expressing his affection for her, and praying for her guidance. Furthermore, any worry or sadness that afflicts a believer expiates his sins, so your sister's ill-treatment might be a reason for the expiation of sins. Instead of praying for death or evil, it is advisable to pray for a righteous husband for yourself and for her, so that the animosity may cease.