I have one dog that has an extreme case of separation anxiety. When we first got him, I would confine him in the kitchen when we left to go shopping and leave my other dog with the run of the rest of the house. (I did this mainly because at the house he lived before he came to us he had ingested inedibles and required emergency surgery because of an intestinal blockage.)
Even though we would only be gone for a short time, he had a difficult time, barking to show his anxiety. Finally, I put the other dog in the kitchen with him. He did a 100% turn around. So then I tried giving them both the run of the house, and both were happy campers and no one got into any trouble. I know my suggestion may not be practical, but the company of another dog was the answer to my dog's separation anxiety.