McVeagh was married to character actor/director Clarke Gordon (her fourth husband) at the time of her death. She had four children and nine grandchildren. One of her grandsons, Dr. Paul Robert Appleby, PhD, who was raised effectively as McVeagh's fifth child, is a Research Scientist and Assistant Professor at the Keck School of Medicine and at the Annenberg School for Communication and Journalism (both at the University of Southern California).
