...It is the Umpires job to keep this from not happening....
This would be incorrect. The umpire should be concerned with the game on the field and those participants. The "fans" and spectators do not exist. If a fan or spectator chooses to make his or her presence known by threating behavior, loud profanity, addressing players personally, or coming onto the field, it would be the job of the tournament director or some other administrative personnel to deal with the idiot....er, fan.
To MandM....once this person started on your DD personally, you should have alerted the tournament director.