I thought it was all the step-mother doing? Maybe she used his father name as a cover up

Nahh. His stepmother wasnt as evil as his own father

His step mother only planned the shooting at ML's home (their target was Ian/Jakyung). Refer to the previous chapters when she also asked the other brother (Taehan) to join her plan. The killing mission MC carried from the beginning was really planned by ML's father