Hmmmm.
It's hard to know where the temper and explosiveness has materialized from here recently. Divorce can be traumatizing to children. She's been through divorce; it happened at age 4. When she was that age, she probably felt her world was crumbling down around her. Trauma. I think a good child counselor/psychologist would be very beneficial in unlocking the "whys" without re-traumatizing her in the process and helping her get some stuff on the road to healing. Also, maybe there is stuff going on at her mother's house that is causing this. You don't know what all goes on there....but you have indicated a few things here that would lead me to believe it's not very good. Wounded creatures tend to lash out.