It sounds like your sister is basically telling you to alpha roll the dog, which I wouldn't do.
I don't advocate 'beating a dog' obviously, but I am not known to be a purely positive trainer either. It totally depends on the dog.
While you may not want to really get on her (and I don't mean a physical beating), about her behavior with the cats, you may have to. It's not about "you" it's about the dog and what training method works for her not you
My female aussie is a marshmellow, I would never ever use a harsh correction or really stern voice with her, she would shut down in a second..Now with all the gsd's I've had, THE LOOK, does it for them, I can use my voice to get across when I say knock it off, I mean it..and it doesn't have to be a physical thing either.
I can't tell you what to do with Zelda regarding the cats, some dogs are NEVER going to accept cats and that's just the way it is..
You may want to go a certain way with training and that's fine, but it's going to depend on 'her' as to what will work and what won't..
In general I don't know why people are afraid of correcting a dog that needs a correction (again I don't mean a beating or hitting etc)..There are some dogs that are sooo strong willed and determined / thick headed, that getting something across to them means a correction..
You don't need to be dominant, you don't need to be the "alpha", you (general you here), you just need to be as determined as they are and figure out what method is going to work for the dog....respect on both sides.
These dogs are not marshmellows, nor are they supposed to be..
I would find a good trainer who knows gsd's in your area to come in, evaluate her and give you some tips..
Just my 2 cents