How to deal with a truly toxic sibling and not just an annoying one is you don't. When they host some great big event in their great big event I'm hosting oh look at me and see how s/he's not the one hosting it, I am attitude, you don't have to go. You don't have to address rumors. You don't have to do anything but love them from a distance and pray for them. If they are on your front lawn saying, "I know you don't like me, but here's what I think," don't contradict or agree with them. Just listen and keep your hand on your phone. "Oh, Mom's calling." "Oh, my boss is calling." At another time when it's not so toxic you might mention to them that you would prefer they only contact you on the phone or something first.