You need to protect those little dogs. Flinging a dog by the neck is serious. She could break her neck in a heartbeat. Seperate them with a baby gate. You need to teach your GSD to be "gentle." Hold a pup on your lap and show your GSD what you mean by gentle. When she does one gentle move, reward her. Talk calmly and in a low voice. When she pokes or paws, getting even close to rough, isolate her in another room immediately. Anytime she has even the intent (watch for it) of getting too wild or rough, calmly, matter of fact, not punishingly, take her into another room without speaking to her. Leave her for 5 minutes and try again. Repeat as often as necessary. Let her know that to be part of the group, she can't act that way. Don't forget this: Dont' forget to reward her amply, lavishly when she shows behavior you like. Seperate the dogs when you're not right there sitting with them. All it takes is one big mistake and you'll have a dead dog.
I showed my Doberman what I wanted when he was very young by getting down on the floor with them all, taking him over to my Chihuahuas and literally patting them myself, ever so lightly and Lyric (the Dobe would be right there with his nose) I'd say, "gennnnntle" and if he nosed gently, I'd tell him how wonderful he was, but in a quiet, calm, drawn out voice. You want to get him in a calm mood so don't use excitable tones. When he got going with his paws too much, I'd sort of catch up my breath like "heh heh, ooooooo (extreme cautionary or worried sound and very quiet) gennnntle." It took a few months till I could trust him alone with the Chi's. He finally understood and is wonderful with them. It may sound like a silly way, but it worked. I never got rough or angry with him. You don't want to associate a rotten time with your other dogs.
I've shown these a million times before, but I don't think you saw them, so here you go:
Doberman eats Chihuahua
Chihuahua eats Doberman