[Eternal]

I think time is one of the main factors here. Trying to convince her will help, but I think it will mostly take time before she realizes that you aren't going to hurt her. When you do have a talk with her about this, just stay calm and keep it civil. The next time that you have a big fight and start getting upset, try and just remove yourself from the situation and go for a walk to calm down. While its great that you don't punch things very often when you're mad, its still not exactly a healthy thing to do and can lead to destruction of objects. If she doesn't see you punching any more objects, it can help her to see that you aren't a violent person and you aren't a danger to her.