First, locate a behaviorist. One that knows
GSD and working breeds. This is the cynic in me and through my own experience; you will have to search to find a qualified one. Talk with many, verify their experience with past and current clients and be sure you are comfortable with them as well.
Transporting your dog; have her harnessed in, preferably crated in your vehicle. That way you will avoid her pushing past you to get to another animal or child.
Harnesses can be backed out of, haltis won't give you enough control, chokes will cause damage with the lunging. Prongs may or may not increase the aggression, and can occasionally come apart. With my dog, I use a prong with a back up collar. Used appropriately, a prong isn't cruel.
It will take someone seeing her and her behavior, along with your handling to give concrete direction. It appears you have a prey drive at work, and dealing with some fear aggression.
Wanted to add, this may give you a start in locating a behaviorist Certification Council for Professional Dog Trainers®