It's hard to do all at once. I am not sure if you have ever explored the root if these feelings in therapy. I used to feel that way and it stemmed from the neglect I endured from my mother. It took me a long time to admit that to myself. Sometimes we hate ourselves because we feel too guilty to be angry with people close to us. But when I finally admitted to my anger and worked through it, the self hatred gradually went away. But it is a scary road and you have to be willing to walk it. I always felt I expressed myself better in writing. I write my mom many letters that I never actually have her. My brother too, because I felt guilty over abandoning him. Eventually I confronted my brother and apologized in person.

You can use coping skills all you like but if you never confront the root you may never truly feel better. But you might, I can't speak for everyone.