As Gothel grew older, she realized that her Mother probably killed her father, because as a little girl, she saw how they fought and how her mother made late night phone calls to some unknown man.
Part of her anger towards the killer is not only because of Theodore's murder, but also because of her father's murder as well. Obviously, the killer is not Gothel's mother, but Gothel has had anger towards her mother for killing her father for the longest time and now a lot of that rage is being sent in the camp murderer's direction.
This huge, but subconscious factor, plus her main focus; the huge, heart-wrenching factor of Theodore's murder, a man she practically loved, equals a burning heap of mad rage towards the killer. She wants to avenge Theodore's death and subconsciously, even completely unknowingly to Gothel, she wants to avenge her father's murder as well.