Dear :-),
Although you have not chosen a pseudonym name for yourself, you really sound unhappy with your mother’s actions which you described as “abusive”. How do your siblings feel about it? If they, too, are upset with this, would it be something that you all would want to raise with her? Is your father able to lend his voice if he feels the same way too? There is strength in numbers.
I am suggesting this response because trying to ignore or walk away from your mother may not address the behaviour and can have the opposite effect. This is because she may resort to sending her messages of disapproval more openly or intensely or misinterpret your response as being rebellious towards her. This makes your response the focus of attention instead of her ill behaviour.
Your mother seems to do these hurtful actions whenever you are in public. You mentioned that it may be because she wants to look like a mother asserting her authority. Could this reflect her own sense of insecurity or a lack of self-esteem such that she needs to appear to be in control? This harkens to more than age-inappropriate behaviour on her part but a deeper struggle within herself, something she might need to address with a counsellor or therapist. Not dealing with this may inadvertently lead her to experience fewer close relationships as time goes on.
I hope that your siblings and you will be able to do something instead of suffering in silence.