Having big problems with my 1 year old male german shepherd?

You have to get him to a behaviotal trainer ASAP. If this behavior is not corrected promptly he will eventually become an aggressive dog towards humans as well... maybe not towards you, but towards a kid or a visitor. For the moment, you will have to keep him separated from your mother's dogs, and if you plan on putting them together, you will have to watch him like a hawk and supervised during the entire time. I'm sorry to tell you that the problem will now need professional help. Killing another dog is the first step to become a very aggressive dog.