My little girl is afraid of the dark. She won't go down the hallway in the evening, she wakes up once a night to get a back rub to go back to sleep, and the basement...there might as well be a monster down there. I see three ways to go about this situation: disengage and ignore her; forcibly push her into her fear and make her get over it; or go into her fear with her.
Are we engaged with our kids? Do we go into those 'dark rooms' with them? As a father, do you share when you have a bad day? When you succeeded? As a mother, do you state that you are stressed or tell your kids about a victory? Sharing your own feelings with your kids has the power to keep them emotionally regulated, relationally engaged and psychologically healthy (Brown, 2013). Sharing some of your story of being afraid of the dark as a kid will help her connect and ease her own fears. You might find that she starts asking you more often about "when you were a kid, did you..."
Try this simple 'tool' and see what happens. The next time your child throws a tantrum, get below their eye level, talk softly/slowly and empathize. Stay in that position until she feels better. THEN you can redirect, teach the lesson or set the boundary (Siegel & Bryson, 2011). She won't listen during the tantrum anyways, so show her that you want to be there in the ugly as well; that she is lovable when she is at her worst.