It sounds to me like she is bored. German shepherds need alot of mental and physical stimulation or they will become destructive. Give her LOTS of toys to keep her busy. Kongs are GREAT. Just fill them up with peanut butter or cream cheese and treats, and they will keep themselves busy trying to get it all out. You could also get one of those balls that you put treats in -- the dog has to figure out which way to roll it to get the treats out. Nylabones are good for chewing -- GSDs are very strong chewers, so I'd recommend a Galileo Nylabone. Is she crate trained? When she is unsupervised you should crate her so that she doesn't have a chance to destroy things. It's a great housebreaking tool. You could also buy a plastic pool and fill it with sand. Praise her for digging in there rather than digging on your yard. You could also lay down chicken wire -- it will hurt her paws when she tries to dig.

I wouldn't try cayenne pepper. I don't think it would work well and it could be potentially dangerous. If she likes to steal food off counters, I would recommend putting salsa on that food. I would stay away from cayenne pepper though.

I would also recommend obedience classes. They will keep her busy, help you bond, provide her with some mental stimulation, some dogs to play with, and it's a great credential to have.

Good luck!