German Shepherds are working dogs, she needs a job and exercise. No not literally a job but a task that she can do to occupy her mind because this breed is super smart. Otherwise dogs of this breed get bored and show neurotic behavior. Excessive barking, licking, chasing her tail, and things like that. Sounds like right now she sees her job as protector of the yard and home. Try giving her toys that she has to figure out…a kong with peanut butter inside or a treat ball that dispenses treats when rolled around. A fun activity for her with the kids would be for them to hide treats around the house and have your dog sniff them out. Also, this breed needs to be walked…a lot…again you having a working breed dog. If the dog is kept in a pen or inside a house all her life without exercise and daily interaction with her family she will have behavior issues. Like someone else mentioned your dog may be great at agility which is both a job and exercise! Last, a good quality food like Wellness or Canidae can do wonders…it ends up being cheaper than you think because you feed them so much less of the quality food than of the cheap stuff, plus it means much less poop in your yard.
We invested in a trainer for a past dog and it totally changed the way we saw and trained our dogs from then on, we too love this breed and all breeds from the working class. That dog was a lot like you discribed of yours; she always wanted to be outside and cased the perimeter of the yard barking like a mad woman. Inside she was also in mischief tearing up toys, pillows, jumping over furniture. She too was super skinny and we did up her food a bit. After we completed the training program with her she was calm and obedient, she was like a different dog. We just did the things I have mentioned here.
Right now we have a Golden Retriever that once nobody wanted and was given back to the rescue twice. He is now a relaxed happy obedient boy because we invested a little time training him and giving him a “job”. Good luck!