I am so sorry to hear this. I feel terrible for this dog. It isn't his/her fault! German Shepherds are very intelligent highly trainable dogs, but because they are so smart, their owners must be careful to not be the one being trained instead of the other way around...
Your parents have failed this dog. They need to step up and take control. Since they haven't, this dog has. That is what all dogs do. If there is no pack leader.. they BECOME it.
Your parents need to watch the Dog Whisperer and learn some things about their role in all of this. Reading a few books on the breed wouldn't hurt either. In the meantime, I would not have my tiny kids at their house.
We have a German Shepherd that I would trust with any child. When she was a puppy, she too would run down the halls with our kids and try to herd them... it was playtime for her. They are nips, however, and not bites when they are doing their herding. She doesn't nip anymore... just runs with them.
The nipping when handing the baby over is much more troubling. Our GSD will sit and watch my nephew wallow all over her bed (the dog's bed) and look to me like "What do I do?? Is this okay?" She licks them (other friends' babies), or gets up and walks away, and sometimes both. Generally the biggest problem is that she might knock an early walking toddler over with her tail...lol. The older kids... she thinks she is one of them and is right in the mix with them. And she gets excited and WHINES when kids come over... because she knows it is gonna be exciting and lots of running around playing. ALL kids, she is very protective of (not possessive... it is not the same thing). But adults... she is much more cautious about.
These dogs have some amazing abilities and certainly can be wonderful family members.... when they are properly trained and understand their place in the pack. (And I wouldn't be surprised that the dog has learned a way to open it's kennel, depending on what kind it is... ours can open her door at the kennel where she is boarded when we travel... and she has done so and let other dogs out as well...lol. They have to double lock her kennel now. She also figured out how to open a friend's fence gate after we put her out in their back yard during a visit once. It took her about 4 minutes... and she was sitting on their front door step looking in at us... their dog was still in the back inside the fence. We put her back in the back yard thinking the gate must not've been secured properly... and watched... she opened it again and went right back to the front door because our kids were in the house. Their dog still to this day hasn't figured out how to open it). She also can open doors in the house and has let herself in through the garage from outside more than once. (the kids were out playing and she was thirsty.. so she came in to have a drink, lol).
The first step to Mom getting a handle on this is to take the dog for daily walks, and ensure that MOM is setting the pace and not getting dragged around. There is a right way and a wrong way to take a walk with a dog. The dog may have been through a training class... but if you don't practice the discipline at home on a daily basis... it means nothing. They must exert their authority over the dog or the dog becomes the authority. And they can be dangerous when they are the ones in charge... not because of evilness or meanness.. but because dogs behave differently than humans instinctively, and they have powerful jaws.
Post "So What Happened" comment:
Glad to read your update, and to know that Dad has a handle on things. The only thing that seems to be missing is that Mom sounds like she let Dad handle it. Ideally, the should have taken the dog to classes together, so that both of them learned the skills to handle the dog. The dog sounds like it recognizes Dad as the Alpha, but not Mom. That needs to be corrected, and the only way for that is for Mom to take some training-- with or without the dog accompanying her.
I would suggest also, that if getting to a training class is difficult for her, that she at least invest in a book on training and read it. I recommend "How to Be Your Dog's Best Friend" by The Monks of New Skete. It is chock full of information. Also, watch Cesar Milan on National Geographic Channel.