In my mind, the external conflict between mother and daughter exists on two levels. The first is that Lady Capulet has no problem seeing to it and expressing to Juliet that she wishes for Romeo's death. The idea that she seeks to obtain poison to use against Romeo is something that naturally causes a conflict between both of them. Given daughter's love of Romeo and mother's intense hatred for him, an external conflict is evident. The larger issue that presents itself in this scene is that Lady and Lord Capulet have arranged for Juliet's marriage to Paris. In this, another external conflict is evident because Juliet does not wish to marry him. It is here where Juliet speaks the idea of not being a "joyful bride" if she is to marry Paris. The primary conflict here is one in which the mother and father want something that the child rejects. This helps to set in motion in the intensity of emotions in this scene and the hardening of sides for both. The external conflict manifests itself in clearly defining where Juliet and her parents stand and this is in pretty strong opposition to one another. In this, the external conflicts help to create the chasm in which both child and parents exist apart from one another.