It sounds as though she has an extreme case of separation anxiety and unless you are confident in your abilities to retrain such a dog I think you are going to need to contact a dog behaviorist.

The only thing I can suggest at this point is to see how she does when confined to a small room (laundy/bath) that opens to the main living area. Install a gate in the doorway so that she can see and hear you and the other dog, then start feeding her in the room with the gate always open. I suggest you also place a dog bed in the room so that she sees it as a safe place to hang out. Once she appears comfortable eating in the room (this may take several days or longer) close the gate and watch for any signs of stress. Don't baby her or talk to her when closing the gate.....in other words.....don't make a big deal out of it. If she likes food, reward her with some small liver bits when she's quiet and not showing signs of anxiety. If she likes toys or chews, give her one or more of those and if you think having the other dog with her lessens the anxiety, then leave him with her in the small room.
It's possible that you may only be able to leave the gate closed for a few minutes, or less. If you see signs of her anxiety building up when you close the gate, distract her or give her a command to sit, reward her for obeying the command, then open the gate. You could start with one short session a day and over time increase the time the gate is closed. Increase the time only if she's showing improvement.

Here is a link that might be useful: Separation Anxiety

This post was edited by annz on Sat, Nov 22, 14 at 12:42