I’ll weigh in on this, though I might be a non-CMish voice in this matter. I am a left-handed adult, whose writing was barely readable until I was an older teenager. This was not for lack of trying; I was and am a voracious longhand writer. Even when I was in elementary school, if given an assignment to write a paragraph about something, I would write pages. I suspect my teachers both dreaded and welcomed it; my creativity was boundless, my penmanship….yeah. (And this was in the days before assignments were typed as they are now, even when I was in high school) I don’t blame any teaching method. I don’t know why my writing was so poor or why it improved to the state it’s in now, which is readable and even semi-attractive.
But I will say that what you’re describing with your daughter’s writing habits was and is me to a T, and this characterizes my left-handed friends, too. The page looks different when you’re using your left hand, and the strokes just feel better when reversed. The left-handed brain works differently than the right-handed one, I know it’s not the “right and proper” way to write and I was probably corrected repeatedly. Someone who has more knowledge and experience teaching writing will hopefully chime in here. But if it were me, given all else you describe, I wouldn’t make it a hill to die on.