From what you described, it sounds like your cousin suffers from NPD, narcissistic personality disorder aka "emotional vampire", one who s*cks the life out of others by being so demanding and always blaming others, never wrong, can't apologize, etc.
When she was in a rage over your response and her behavior (controlling, influence), that is called a "narcissistic fit". These types of people have difficulties in any and all of their relationships because they are demanding, controlling, self centered, self absorbed and uncaring of others feelings, all behaviors that alienate other people who run for the hills and hide.
I hope that enlightens you about her personality issue.
You handled the situation gracefully.