Try not to give up on her just yet. A pound is a scary, unknown environment for a dog and she probably feels absolutely all over the place. Many dogs act differently to when you first met them once they are in a new home and start to feel comfortable. As a pound dog, she could have any sort of history that has made her how she is.
As well as going to training classes I would actually invest in a canine behaviourist who can assess your dog properly. Training classes are just that - training, but a behaviourist (a good one) actually has the know-how to get into the mind of the dog and figure out why she's acting like she is and how to fix it. Consider it like a doggy psychologist.
Another thing, I wouldn't recommend leaving a new dog to have the run of the house while you're out. Even a 'normal' dog can get bored when left alone and an outlet for that may be being destructive. I would restrict her to a certain area of the house where she can't do much damage (ie, a laundry or bathroom) and also start crate training her. A crate trained dog is a wondrous thing and very easy to take or keep anywhere.
Here's some info on crate training:
https://www.apdt.com/veterinary/assets/pdf/APDT_CrateTraining.pdf
Just remember, dogs are complex little creatures with their own feelings and emotions. They too can have mental issues because of negative things that have happened in their life, but can only tell you how they feel in their own language. It's just a matter of learning that language and becoming a pack leader that they can trust.