I rehomed a female gsd that as you say, just wasn't a good fit for a lot of reasons. I think she let me pet her a total of 3 times and that was only when she was stuck in the laundry room with me and had no choice. She was fantastic at obedience, a beautiful dog but we had absolutely no connection. She had a very high drive and needed a job- she would have made a great police dog or drug dog. I ended up finding a young couple who advertised online that they were looking for a female companion the same age as their male gsd. When they came to look at her, she was a completely different dog! She loved the guy, adored their dog and I've never seen her so happy. She couldn't wait to jump in the truck with them. That night they sent me a picture of her using their dog's head as a pillow. The guy's parents have a ranch so she gets to go herding, they run a lot, live on a lake so she can swim. She has a much better life than she would have had with me. I took a lot of flack for finding her another home (my mother didn't speak to me for weeks) but I know I did the best thing for her.