When it comes to overcoming the dramatic way in which your dog deals with your disappearance, behavior modification is key. In some cases, medications may be necessary as well but that should never be the first line of defense - nor should medications be used without proper behavior adjustments.
The first step is to adjust how you interact with your dog during their frantic periods - this often means ignoring your dog if they are attempting to get your attention in inappropriate ways. Not looking at, talking to or touching your dog until he has calmed down will help reinforce the type of behavior we want to encourage. When starting this approach, it is not uncommon for dogs to seem to 'up the ante' in therms of their inappropriate behavior. This is called an 'extinction burst' - it is important not to become frustrated or feel sorry for your pet during this time. Rewarding any type of anxious or attention-seeking behavior is sure to prolong their separation anxiety. Once your pet has calmed down and you have determined that they are no longer frantic, it is important to reward them with love. Often I will encourage my clients to get their pet to sit or lay down in order to receive attention. Routines surrounding departure and arrival will also need to change - one suggestion is to withdraw attention from your dog 5-10 minutes prior to leaving and waiting for them to be calm upon arrival home. The goal is for departures and returns to be considered 'nonevents' by your pet.
When leaving your home, providing an appropriate distraction to your dog may help divert his/her attention from your departure. A puzzle toy full of treats, a kong toy with peanut butter or yogurt, or a favorite chew toy can provide a positive association for your pet in regards to you leaving the home. I encourage clients to save this particular toy/treat for these departures so that your pet only receives it during these times. Setting up cues for your pet will help your dog feel more comfortable when you are gone - ask your pet to go to his/her mat or crate and then calmly provide them with their special toy/treat.
When coming back home it is just as important to refrain from overly emotional greetings - walking in matter-of-factly, setting down your belongings and once your pet is calm, then greeting them will help to make this time a normal event.
One of the things I have learned during quarantine time is that we are home.... a lot! Our pets have become accustomed to our presence and for those of us who got puppies during this time, it sets up a false sense of reality for them. When starting off with a puppy its important for them to spend some time home alone so they can get the sense that they are just fine without their human counterparts. It's also important for our pets to learn to spend some down time by themselves, with us at home. This can be done by encouraging your pet to spend some time on their mat/crate with a special toy and treat while you accomplish some tasks around the house or watch a favorite TV show. At our house, our puppy has learned that at dinner time he spends some alone time in his crate - some days he loves it and other days its a work in progress but we are working to consistently provide him that down time.
Separation anxiety can be a very frustrating problem to deal with but with some simple behavior changes and consultation with your veterinarian, your pet can learn to love being home alone.