German Shepherds are an amazing breed of dog. They are clever, loyal, sweet, and designed for daily stimulation and work. A German Shepherd who is neglected (I'm using this term loosely), is a dangerous dog. That breed, in particular, NEEDS to be part of a pack and to get a mental and physical workout every day. If not, it can start having some serious behavioral issues.
It doesn't seem like your dog is THE issue. Your and your husband's relationship/dynamic seems like it needs work and the dog is an easy target. The dog, for you, seems to have become the symbol of an imbalance in your relationship.
Here is what I suggest, in relation to the dog. Sit down with your husband. Kindly explain that the dog is not being treated fairly. It doesn't sound like a happy life for ANY dog, let alone a large, active breed. It lives in the backyard and is not trained or played with/loved on/disciplined/exercised. The current arrangement is not fair on the DOG (or, by the sounds of it, you - but it might be helpful to keep the two issues separate).
Then set clear and reasonable goals. Here are some examples:
-Dog gets run for one half hour a day, minimum. Husband takes it for these runs.
-Husband reads a training book (or three) and starts applying the techniques he learns every day. The dog should get trained (throughout the day, everyday - but that's probably not reasonable) at least once a day for twenty minutes.
-Husband is responsible for feeding, watering, grooming and porch sweeping.
Then set a timeline. If, for example, in two weeks, your husband has not been able to follow though with the BASIC upkeep of this animal, the DOG needs to be given to a better home. There are German Shephed Rescue groups that will find it a good home. http://www.gsdrescue.org/