There isn’t much that can be done to overcome the bad relation, in my opinion. You could involve the Quality Department as early as you would like in the Project Life, but that wouldn’t change much (if anything). The people in the other departments may not agree with the regulations set forth which quality has no control of. There is bound to be some resistance, but quality just has to stand its ground and take the hits. I guess the only effective way would be to get to know the people in the other departments on a personal level. Allow them to see you as a person and not a department so that when certain things have to be done, they look at it as you are being forced to have this done vs you are being a jerk and making them do things a certain way.