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When a dog is well-behaved when people are home, but destructive when alone, it is almost always separation anxiety. Every one of the behaviors you are seeing is a sign of separation anxiety. You’re dealing with one of the most frustrating behavior problems. With consistency, time, and patience, you should be able to reverse this behavior. If you don’t get good results, or you don’t have the patience for this type of training, you can speak to your vet about medications that may help. Anti-depressents help some dogs, and sometimes sedatives are used. You can read more about separation anxiety here:
Helping a dog with this disorder is much easier if the dog feels safe in a crate (kennel). This amounts to teaching her that the crate isn't a bad place. Put the crate in a pleasant area of the house, not off in some corner. Begin by calling your dog into the crate and giving her a very special treat of some sort. Don't close the door. Let her eat the treat and then leave. Repeat this over and over. When she goes into the crate willingly to get her treat, close the door for just a few seconds and continue to give her treats while she's in there. Repeat this until she doesn't seem to mind. Gradually increase the time. Speak cheerfully and praise her all the while. When it's not a problem to leave her in there for about 10 minutes, start giving her a filled Kong toy (sold in pet stores) in the crate. It will take some time and patience, but she will learn to view the crate as a place where good things happen. Continue this only when you’re home, until she doesn’t seem to mind the crate. When you're ready to leave her in the crate when you leave, give her the Kong in the crate before you go. The first time you go, just walk out the door and then and then return. Gradually increase the amount of time you’re gone by only a few seconds at first, then a few minutes.
There is also a product you may want to try. It contains calming pheromones, and is called Comfort Zone. The pheromones are natural substances which have effects on animals. Comfort Zone is available as either a sray or a plug-in diffuser. The diffuser would be longer-acting, and better for your situation.. Many people who have used it for dogs with separation anxiety have reported good results. However, the pheromones alone won’t do the trick. You’ll have to use them along with the measures described above. Pheromones may make it a little easier.You can read more here:
I know this sounds like a challenging task. It is. Not everyone is up for a dog training task like this. If you feel it is too much, you could speak to your vet about medications, or you may make the decision to return her to the rescue. If you do that, be sure to let them know she has separation anxiety. She is not deliberately misbehaving or being destructive - she is terrified of being alone.
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