One would hope that the parent has the child's consent to the hairstyle change, or that a stylist would not force a major change upon an unwilling child. But that aside....

Unless something within the divorce judgment restricts a parent's right to get the child a hair cut or style when the child is with that parent, then the parent has the right to do so. Even if the child is begging for the new style, mature parents will discuss significant changes before getting the child's hair cut (or permed, or dyed), as it's an obvious point of potential friction or conflict. But, at the end of the day, cut hair will grow back, dyed or permed hair will grow out, and life goes on.