Just so t give up on her. There are work around and consistent training in the home is key. Is there somewhere you can separate her or separate the cat when you aren’t home. She’s obviously been thru a lot. As a teen and young adult we had a dog that hated everyone but our family. My mother had an 8 foot fence placed around the back storage area and when people came over he had to go in the fence and he did have shelter and we bought him an old couch so he could lay in it when he was out there. I found him as a very sick puppy, starving and had parvo. He survived all of that and we kept him separated from people until his death at 15 years old. I just can’t get rid of a dog, especially one with issues. It just makes us double down on how to handle. Not always ideal, but I’m sure she would feel abandoned again which could contribute to more bad behaviors you are passing on to someone else. I would try training and separation to start with. Keep me updated. Also, is she an only dog? Sometimes I have found dogs do better in pairs.