It seems you may have gone offline and I will soon have to go off for an appointment so I have been working on your question with other suggestions as well as explanations to why we do certain things with dogs that have anxiety.
If you have any questions on the below please come back and ask and I can explain further when I am next online. Give the links a look over so you can get a feel for what needs to be done. Remember that a dog that was a rescue has a past that no one knows about and one cannot know what may make an imprint that will have the dog slide backward a bit.
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DR RB gave you some sound advice and I would just like to add some other solutions that were not mentioned above.
Yes you have to practice the above on a daily basis and basically change your whole routine daily so the dog never knows when you are coming or going, Ignore the dog for 15 minutes before you leave and after you come home. You are correct, your dog knows your routine very well and has memorized every detail of things you do before you walk out the door , right down to the coat you may wear to work as opposed to one that you wear to take out the garbage and this is why it is so vital that for a long period of time you must change up your routine on a daily basis.
Along with that you need to train the dog positively so you build up the dog’s confidence. Think about a shy person who is suddenly tossed into the middle of a party. They have not been given the skills on how to handle that situation. You must build your dogs skills to be without you. So daily training positively helps boost the confidence the dog needs, and you need to practice alone skills which would consist of getting a firm down stay on the dog’s bed as you are able to move further and further away from the dog until eventually you are in another room for a second, then come back and reward the dog for that alone time. Gradually you want to build up the time you stay out of sight. This helps the dog to build a sense of self assurance.
It does sound like he has a very bad case of separation anxiety so this will not be solved over night and figure a good six months of daily training and confidence boosting before the dog is comfortable to be alone. Also know that even after the dog is okay with you leaving, that it can slide backward if you stop daily training. This is because dogs go through imprint periods of their life, one of the imprints that are repeated through a dogs life a different intervals is a fear imprint. So if you think the dog is okay to be alone and you stop the obedience training, you could leave the house, there could be a large truck or construction starting on your street which brings with it a loud noise , and something that simple can put the dog back into a fear imprint.
As for medication, there is an over the counter med in the vitamin aisle of your drug store called melatonin. Melatonin works in conjunction with what the brain already makes, serotonin , but does not make enough of which causes the dog anxiety. The melatonin will not drug the dog, but it will add the extra serotonin the dog needs to help keep from being anxious. So you may want to give that a try. This works great for noise phobias as well.
There are other products to try to help calm a dog and I am going to put them all below with links.
Even with a change in routine, the melatonin and other suggestions below, the most important thing to do is continue confidence building through training. Eventually you can scale back on the amount of times a day you do this, but is should still be done daily even if you can only fit in 10 minutes. I am going to direct you to clicker training as well which is easy to follow and if you cannot do each and every command daily at least get a good down stay. The key is you want to set the dog up to succeed not fail.
You can try combining many of the below items. The calming music works well especially for any noise phobias and just has a calming influence over the dog. This is used in many kennels where anxiety is high.
video’s to see how clicker training is done, scroll down to videos http://www.clickertrainusa.com/clicker-training-videos.htm
Melatonin found in drug stores by vitamins
Through a dogs ear music
3 hours of dog calming music on youtube to try out
mind stimulating toys
talk to me treat ball
Kong these work great when stuffed with cream cheese and frozen
Dog Puzzles. If you just type in dog puzzles on amazon you will come to a page full. I just happened to pick this one . PetCo also carries dog puzzles.