A class with six dogs in it is exactly what you need to do. That is enough for the distractions, enough individual, enough people, enough space.
This is not going to be easy to hear, and may not be popular here, but, this is my take on this: I really do not care what the teenagers did, that one incident should not have caused your dog to become what he is. Your dog is a young fear-reactive dog, you can call it weak nerves, whatever. In my opinion, you should neuter this dog if he has not been neutered already.
This is also NOT the end of the world. Your dog can make GIANT strides. And you will learn too how to manage situations with him in it. The training, and plan on continuing to train for a year. Classes once a week. Just keep signing up. The training will help your dog's confidence in YOU, and You will improve your confidence in your dog and in yourself. Keep on going, and I will be very surprised if you read this thread 12 months from now, and you are not in a whole other universe.
It may be that your parents will never feel comfortable around your dog. They are in their seventies and a dog bite takes a lot of time to heal, and longer for older people. You may choose to board your dog if you spend the night over there. Or if it isn't too cold, and you have to go some to get too cold for a GSD. Take the dog and leave it in your vehicle. You can go out every 2-3 hours and take the dog for a quick walk. But do not force the dog on your parents.
Just taking your dog out and exposing them to people and places isn't enough. In fact, it can be counter-productive if your reaction to people and places causes him to be more wary. It is hard to not be nervous when we are afraid our dog might lunge and bite someone. That is scary. So cut that out. Take him to classes. Work with him. Throw the ball in the back yard for exercise. Take him on walks only if there isn't a lot of distractions and people, go late at night, early in the morning, or drive him somewhere if you must.
Remember that you are not just managing him, or hiding him at home, you are going to classes. Your dog is learning to trust you and gaining confidence, you are upping your leadership skills by reading/learning/practicing good leadership. NILIF might be a good place to start.
If you do not give up on this dog, in another year, you will be at a different place. In two years, this dog is going to be even better. But, to get to that place, you need to change what you are doing right now. Walking him with your hands down at your sides, where you need to correct more -- that is not what you need to be doing. Let them teach you how to walk him. How to teach him to walk on a loose leash. Be open to different types of collars. A prong collar may be the right choice with your dog. It might be the wrong choice. Treats may be the right way to go. Corrections may shut your boy down, and they may be what he needs. Under the careful eye of a good trainer, they should be able to match you and your dog with a method that gets good results. It isn't one size fits all.
He will mature, and your leadership will improve, he will gain confidence in himself, you will gain confidence in him, he will learn to trust you, and you will learn to trust him and you will learn to trust yourself. And there will be a bond. You will automatically set your dog up to succeed and will automatically praise him for doing so and that bond will grow. You will automatically tweak the situation you and your dog is in so that it is imperceptible. And negative behaviors will go way down.
It isn't over night. Keep a diary. In three months, you should see a difference. In six months even more. In 12 months, I will be surprised if he isn't a different dog.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC