Yeah, this is separation anxiety. What does she do after you leave, though? Do you come home to a trashed house, chewed stuff, "accidents"? Does she howl and bark until you come home? And what do you mean by "throws a fit"?

This isn't a problem I've had with any dog, mostly because we rarely start with a rescue (although we have), and we just don't go anywhere that often. All the dogs would like to go with me when I go somewhere, but they all accept being told "nope, stay here and guard".

But my second son and his wife adopted a dog with SEVERE separation anxiety issues- Tucker was so bad that two other adopters gave him back within a week. He would TRASH the house... chew walls, couch cushions, carpets. He is also a hoarder... he would steal a loaf of bread and HIDE it in a chair seat... only to be found weeks later, blue with mold! It took them about two years, but they CAN leave him now (they both work, so they don't have a choice) and not come home to a trashed house.

For milder cases, simply desensitizing can work... going through SOME of the motions of "leaving for town"... without actually going anywhere... can work. It does take time, though. You put on your coat, grab your keys- and then go watch TV! Or carry the car keys with you (clip them to your belt loop or something), jingle them occasionally... but don't leave.

It's also vital that you NOT make a big fuss when leaving- or when you first come home. Dogs often interpret our "excitement" as "reason to worry"... spending a lot of time "reassuring" them when you're getting ready to leave gets translated as "this is a BIG deal. I might not come back home again".

IF the dog settles down within a few minutes of you leaving, it's not a big deal, unless she's getting worse. One thing that quite a few trainers have found really helps is having a "special" toy that you only put out when you're leaving. There are "kong" feeder cubes... specially designed to "reward" a dog which plays with them by releasing individual kibbles. Giving one to the dog JUST as you walk out the door (and then collecting it when you come home and putting it away until next time) can often distract them enough to get "over the hump" of you leaving.

Playing a radio or leaving the TV on when you leave helps some dogs...

Crates... crates are great for dogs which were accustomed to them from puppyhood. For adults who never were crate trained... not so much. I love a crate in the house, especially if there are kids... I've been telling the puppy buyers who have children to teach the kids that the crate is the dog's "private place" and they should be left strictly alone when they go in to lie down. Handled correctly, the dog sees it as "home" or a sanctuary.

If a dog with separation anxiety is trashing the house, a crate may be necessary. But it's important to remember, this behavior is NOT really under the dog's control... it's a version of a panic attack, and one which hasn't ever been accustomed to a crate may go absolutely berserk if locked into a crate and left. NOT a good thing!

Here is a good article on separation anxiety.
http://pets.webmd.com/dogs/separation-anxiety-dogs

One thing that I would try if I had a dog with these issues- the herb called Virginia skullcap. I've only used it on dogs a couple times- for thunderstorm phobia. But it was absolutely amazing how well it worked- we had an old Border Collie/Australian Shepherd mix and as she got older, she got more and more terrified of storms. She wasn't a housedog, and bringing her in the house didn't really help much... she was generally nervous about being inside, on top of the storm.

But she was getting SO agitated that I was really afraid she'd end up getting hurt or worse (she was about 14 at the time). So I gave her a single capsule of skullcap herb. In 20 minutes- with thunder still booming and lightning flashing everywhere- she was sound asleep under the kitchen table! It was amazing...

So I would probably try giving her skullcap (the "1 capsule" worked on a 40# dog... you could even open one and put part of it on food if necessary) an hour or so before you need to go somewhere. It *might* just dampen her adrenal responses enough to help.

Summerthyme