How can one control oneself and not respond to the harm caused by an older sister, and how can one be patient with her harm? What are the rights of an older sister over her younger sister?

If what is happening from your sister is aggression, then you must strive within yourself to repel the harm and be patient with her, and not reciprocate her bad behavior with bad behavior. This is because the kinship ties required by Islamic law entail being kind to relatives even if they act poorly. The one who maintains ties is not the one who reciprocates, but rather the one who connects with her kin when they cut her off. Your kindness to her will elevate your status, remove animosity, and God will grant you victory over her. However, if you are unable to bear such kindness, and continuing to associate with her causes you harm, then there is no blame upon you for cutting ties with her to the extent that repels her harm from you, for a graceful abandonment is better than a harmful association.