Disabling Children's GUI from script

How would I disable the children’s GUI from the parent’s script when a button is pressed?

You can get to child by pre-storing it from inspector variable, either get it using Transform.GetChild().

public GameObject child; //store from inspector

private void OnGUI(){
    if(GUI.Button(new Rect(0,0,100,30))){
        DisableChild();
    }
}

private void DisableChild(){
    transform.GetChild(0).gameObject.SetActive(false); //This will get the first child
    //OR
    //child.SetActive(false);
}