Allsorts In my view, responsibility works both ways but, in the first instance, parents are responsible for the emotional and psychological wellbeing of their children, to stand them in good stead for the future. It appears to me, from the OP's post, that her mother undermined the confidence and general self esteem of her and her brother, which has affected them in later life.
Of course, most, if not all parents make mistakes - and sometimes bad mistakes - in the way they care for their children. I am the first to admit that I made many mistakes with my first child which I believe affected her ability to cope with life as an adult. However, I acknowledged those mistakes and did my best to be a more caring and supportive parent in later life. Conversely, the OP's mother continues to undermine and manipulate her adult children and, from what the OP has said, remains critical and self-centred.
It is easy to be judgmental about other people's feelings and actions but I feel the OP has gone out of her way to manage a very difficult and soul-destroying situation. She does not need any more criticism - it sounds as if she has had a lifetime of that.