Oh, one other thing. (As DH and I sit here with our once-crazy GSD, also now like a different dog... As we were reading the part about the barking and whining we were laughing cause our DS was coming home from a sleepover and although she knew it was him, she was behind the glass door and wanted to get to him so was barking that higher pitched bark and wagging her tail, completely focused on him and only him - my DH was like, "Speaking of Shepherds barking" lol - she looked beautiful, actuallly
...)
I imagine that last time you had your GSD puppy either you didn't have kids or they were really young. My kids came home to two adult GSDs when they were born, but they were about 6yo when we got a puppy. Even though they'd literally been around GSDs their whole lives, our vet made a HUGE deal about teaching them how to interact with the dog, recommending not letting the dog chase them or bite them, or to play rough with the dog, etc (which I subscribe to also anyway, but it was good for everyone to hear it and be on the same page about it).
I don't know how old your kids are but I'm going to say the same thing to you. You almost have a blank slate with this dog so he's probably not learned a lot about the world (other than the frustrating things). Now is the time, from the get go, to teach him how to be the great and stable dog you want him to be. Don't rough house with him. Don't let anyone growl in his face. He might not know what a ball is but show him how much fun fetching one can be. Teach him to drop it at your feet and then you'll throw it again. (Be careful about taking it from him; teach him to drop it.) Reward good behavior. (I like verbal praise as opposed to lots of treats.) Teach him to respond to your voice by talking to him lots. He'll learn to pick up on your tones and it will open up a great "dialogue" between you as a means of communication.
I'd also probably forego the bones or rawhide type things right now as he adjusts to your home. (Again, high value items a dog is willing to fight for; and he's got lots of "competition" - in his mind - in your home with the other pets and kids, etc.) There may come a day in the future that this won't be an issue, but for now I wouldn't even put them into the equation. (Friends of mine had a very bad situation with an adult rescue GSD, a high value treat, and a child visiting their home.
) Keep in mind that many GSD rescues will not adopt out to homes with children under a certain age, often 7 to 10 yrs old.