Think of it this way.

Your fathers intentions do not matter.

What matters is that you felt your life was in danger. Maybe your father knew all along that he would never kill you. He still terrorized you to the point where you felt like you were going to die.

If you felt like you were in danger constantly, this is more than enough to cause PTSD.

Your father may never have intended to kill you. Your mother may be defending what she thinks she knows. But nobody can get into your head and tell you that you didn't live in fear. Don't ever let anyone convince you that your feelings are wrong. No matter what you feel, it is valid!