There's no way to tell which individual dogs might develop separation anxiety, so it's best to desensitize all dogs to their family's comings and goings. If you're starting with a puppy, you have a clean slate and should be able to progress through the program with no problems. If you've adopted an older Yorkie, the dog could already have a case of separation anxiety. Your training will be a little harder, and your dog's life will require a higher degree of management (leaving him alone as little as possible) while training is ongoing, but you can still succeed in the end.
A dog suffering from separation anxiety needs to learn two things: she can be alone without anything bad happening, and you will always return. So it's crucial that you don't leave her alone for extended periods while you are working on the problem. Take her with you on errands whenever possible.
Symptoms of Separation Anxiety
Dogs suffering separation anxiety experience a high level of stress. They often lose control of their bodily functions, and you may find a puddle or a pile when you return home, generally close to the door through which you departed. This is not a willful act of disobedience and should definitely not be punished.
A dog suffering separation anxiety may scratch or bite at the door through which the person departed. Or he may go to wherever his human's smell is strong, often the couch, and engage in destructive chewing of cushions or pillows. This is another effort to relieve stress. You may also hear from neighbors that your dog howls or barks from the time you leave until exhaustion sets in. Even a dog left inside the house can often be heard outside.
If your puppy insists on following you and being close to you all the time (after you've untethered her), and cries when you're separated, this may be a warning of a tendency toward separation anxiety.
Dealing with Separation Anxiety
Whether you're starting fresh or dealing with a dog already showing signs of separation anxiety, the program is the same. First, use baby gates or an exercise pen to confine the dog close by, where she can see you but not reach you. Ignore her if she cries or whines. Release her when she's being quiet. Only confine her for a few minutes at first, and work up to an hour. Don't be emotional about confining her or releasing her — just go about it matter of factly. When she can be settled for an hour within view of you, confine her where she can't see you, but can still hear you talking. Start over with a short confinement time, and again gradually work up to an hour.
When your Yorkie can be calmly out of sight of you for an hour, begin actually leaving the house. If you haven't had any problems to date, you don't have to confine your Yorkie (provided she's old enough to be responsible). Just pick up your keys, put on your coat, calmly tell your dog goodbye, go out, close the door, wait a few seconds, and come back in. Do this several times a day. Then begin to gradually extend the time you're outside. When you get up to a minute or two, walk away from the house so your scent diminishes. When you get up to five minutes or so, get in the car and drive away, circle the block, and come back. You want your dog to stay calm through this entire process. Keep your departures and returns low-key and unemotional, and build up time slowly, so that your dog can cope.