Moving with pets can be a difficult experience. And the difficulty varies from animal to animal. Not all animals adapt equally well (or equally ill) to change of living quarters. Each species has its own evolutionary history and genetic encoding which give rise to unique problems when taking them to a new location. Let us take dogs and cats as examples, because these are the commonest pet species in the US and Europe.
Dogs and cats have different kinds of attachment to their surroundings. Household pets typically experience two major components of their surroundings – the humans who keep them, and the largely inanimate environment consisting of the house or apartment, its configuration and furniture, and so forth. Dogs and cats that live with humans in a house normally become attached to different things in their surroundings.
Dogs are normally attached to their human masters. They orient themselves and their lives around the wishes, commands and habits of human beings. They thrive on our approval, and whether we caress them or cuff them, reward them or punish them, talk to them sharply or call to them in a soft voice, matters a great deal to them. They do get used to the house or the furniture, but they have much less of a problem adjusting themselves to new surroundings if they are forced to move. In fact, there are many popular stories about pet dogs following their masters for hundreds or even thousands of miles, across state and country borders, after they were separated by mistake. Some of these stories must be at least partly true!
Cats, on the other hand, are extremely attached to the house or apartment where they were brought up and where they have lived all their lives. Their lives rotate around the lay-out of the furniture, the configuration of rooms, niches and crannies and so forth. This is because the cat is a hunting creature, much more so than the dog. Cats are fiercely territorial, and spray their urine and strategically display their solid waste to send territorial messages to neighboring cats. Their lives are defined by territorial elements. That is why a cat often gets confused or disoriented and acts funny when you move furniture around the house. When you move house, a cat is much more likely than a dog to remain with the house and endear itself to the next occupants. Much fewer cat owners than dog owners are truly successful in carrying their pet to a new location and getting them used to it.
One of the major problems that people face when moving with pets is getting the animals to re-learn their toilet training. Both cats and dogs get used to getting rid of their waste in certain portions of the house or the immediate outdoors, and they have considerable difficulty in re-orienting themselves to their new location. Often they will leave nasty surprises for you on the carpet, near the washing machine or under the sofa.
One good thing in your favor is that pets never quite psychologically grow up into adults, because they are protected from the dangers and struggle of non-domestic adult life. So be a tough parent to them, shaking them by the scruff of the neck if necessary, and they will soon fall in line.