I too have a tricky relationship with my older sister, who has always been bossy and easily offended.
Since my mum died, I have been able to distance myself to a large degree, but still keeping the door open. I had some good advice on GN which helped.
In the end, I have worked out that my sister is jealous of me, although hard to understand, it's the only emotion that fits her behaviour. I can't solve it, and it's not my fault, so I let go of any guilt. Would it help if you stood back a bit and tried a rethink?
My sister was sickly from a small baby, and got used to the attention when she was ill, consequently she relies on her health to get attention, or avoid doing things she doesn't want to.
Her behaviour was very odd when I had any illnesses. I've managed to join up the dots now but the logic is skewed.