Thanks for the additional information. I really appreciate it.
It does sound to me like your new dog is pretty anxious....since you've only had him for a very, very short time, it's definitely possible he may get over this behavior just by watching the way your more confident dog acts, and it's important to remember he's still very much in a period of adjustment, but you're right...it does sound like he's got some separation anxiety going on.
Some dogs develop destructive behaviors such as breaking through windows, destroying crates, chewing holes in walls and destroying sofas in their frantic efforts to cope with feelings of abandonment. Some other dogs may go on hunger strikes or even begin using the bathroom in the house to cope with their feeling of being alone
Dogs with serious separation anxiety issues may need medication as well as behavior modification help from a professional dog behaviorist. Look for a board-certified veterniary behavorist (ACVB) or certified applied animal behaviorist. As for references from your vet. You need solid guidance from someone properly trained to assist you and your dog.
You might also want to consider using a product made specifically for dogs with anxiety. A couple of these things would be:
Melantonin is an over-the-counter drug that can be used to treat some anxiety issues in dogs. The dose you would give would be up to 3 mg given orally whenever necessary up to every 8 hours. More information can be found here: http://www.petplace.com/drug-library/melatonin-melatonex/page1.aspx , which includes risks, warning signs to watch out for and other bits of useful information.
Try a DAP collar. These are collars that are impregnated with a man-made version of the dog appeasing pheromone, which is a pheromone that nursing bitches give off to their pups to help them feel calm and secure. It's something that humans can't smell, but it has an amazing effect on dogs with anxiety and other issues. Although you can find them at your vet's office..you can also find them online at places like Amazon.com and Ebay for much cheaper. Just make sure they're DAP brand, as they seem to work better than some other versions.
When I'm working with an anxiety dog, I generally start with the collar, and then add in the melatonin if I don't see a change within a week or so.
If this were my dog...I'd start with the collar and then go from there. Hopefully he'll become better about being without a human around with some time and direction from your more confident dog.
I hope this helps.