As the mother of an addict, I know that, for me, before recovery I was on a desperate mission of trying to save my son. I would have yelled at anyone who I felt got in the way of MY plan and, sadly, the person I became was a far cry from the loving, caring person I used to be. I was sick, neurotic, angry, scared...no terrified, and totally out of control.
Recovery helped me change all that, I am no longer that awful person that I was (thank you God), and I find peace and beauty in every day...but that took a lot of work and I was willing.
I'm not justifying how your mother is, nor do I think anyone can force her to find her own recovery anymore than anyone can force your sister to find hers. I am just sharing this because I see myself in your mother, somewhere.
When the behaviour of other people affect me badly, I know I need to work on myself and distant myself from them, sometimes for a little while and sometimes for a long time. But I need to keep space between us until we can work on mending our fences and making the relationship work for both of us.
One of the gifts of recovery, for me, was to be able to do that. Being able to be kind to myself and allow myself to stay in the peace and safely of my own life is probably what saved my life and made it worth living again.
Prayers going out for all of you. Addiction truly is a family disease.
Hugs