A substitute teacher is usually a well-trained licensed teacher who is only temporarily filling in for the regular permanent contract teacher's absence. I have known fully degreed and licensed substitutes who make a career out of this, at excellent wages. Don't sell this way of earning a living short. It has many options that the tenured school employee does not.
If I was placing a bet on this situation after reading the summary, I would put my money on the substitute having done exactly the right thing, in view that the mother has never trained her daughter to be obedient when given a command by a legitimate authority.
Perhaps you can learn from this parable, too?
You can't alter a baby's behavior (or a dog's or horse's) by reasoning with it, can you?