I deeply appreciate the love and care you are trying to bring to your sister. Anger comes from a need that hasn’t been met and it sounds as if your sister may be feeling that many of her needs in life aren’t being met. If the anger isn’t the result of drug or alcohol abuse (as it often is) and she is resistant to therapy (which would be a good idea), then you are left with the option of helping her self-regulate her emotions.
I have three recommendations. All three involve you being part of the process of engaging your sister in some healthy emotional habits. The first is for the two of you to take a meditation class together. They are everywhere and finding the most convenient one that has a decent reputation in the way to start.
Secondly, particularly with anger issues, I’d highly recommend a yoga class as this is almost a direct way to begin the process of emotional self-regulation.
Finally, if drugs or alcohol are involved, an offer to go with her to an Alcoholics Anonymous or AlAnon open meeting would be helpful. The culled wisdom of these groups for helping people regulate their emotions is tough to beat.
Wishing you patience and peace,
Proof Positive Blog @ PsychCentral