If my sister does something really nasty to my mom, does my mom habve any right to take her stress and anger out on me?

i dont think so

Hello concerned one usually when people including parents are stressed out about something or frustrated and seems or might be angry and take things out on others especially whoever in their paths it’s not the other person fault or that the stressed person is trying to lash out at you personally of course its-never fair when others do this just try to keep being loving patient supportive and understanding with your mom and pray whatever or whoever is the issue it gets resolved so she and everyone involved can be united and peaceable with each other. Pray for strength to endure and to keep a calm heart.