"Mom always loved you best!"
When dogs are introduced into a cat only household, they often become the primary pet in the owners' eyes. Dogs more aggressively seek out attention, are more demanding of owner interaction, and require more effort in their care with their needs for housebreaking and exercise. Consequently, the dog may replace the cat on the owners' bed, and significantly reduce the amount of time spent playing with and interacting with the cat. The stress of the loss of their territory (the owners' bed) and loss of attention may cause urine marking to occur. In addition, this stress may also precipitate physical illness such as cystitis and inflammatory bowel disease which also contribute to urination and defecation outside the box.
Most dogs do best when crate trained in a household. Even where crating is not used, limiting the dog's access to certain areas or floors of the house is usually very practical. Allowing the cat to have access to areas in the house that the dog is not allowed is immensely helpful at reducing the cat's stress and chance for elimination problems. Make sure that both litter boxes and food and water are available in these "protected" areas. In effect, you are reducing the cat's perceived territory but giving it access all it needs in that territory.
Spending 10-15 minutes a day of one on one positive attention to the cat provides most cats with the human interaction that they need. This attention, including stroking and playing reduces the cat's stress due to its subordinate role to the dog in the household.
Recent research also notes the benefit to the human in petting cats by reducing the chance of death from cardiovascular disease in cat owning patients.
Cat Stool = Doggie Tootsie Rolls
Dogs often find cat stool an engaging snack. To help combat this behavior, people often used covered litter boxes to limit their dog's access to the box. Covered boxes tend to be less attractive to cats than large open litter boxes as they tend to limit movement inside the box and tend to be dirtier since people are less aware of their state and clean them less often.
Limiting the dogs access to certain locations and putting additional open boxes there gives the cat a safe haven to eliminate in peace. Scooping the litter box several times a day not only makes the litter box more attractive to the cat but also removes the stool before the dog can ingest it.
Cat and Dog Households
Safety is an issue in cat and dog households. When dogs are introduced as puppies into households containing adult cats, they will usually accept cats in general as part of the "household pack" rather than prey. In addition, adult non declawed cats are generally able to give significant negative reinforcement (a nice sharp scratch!) to puppies whose behavior they deem inappropriate. Some dogs and cats bond closely or engage in play behaviors that are acceptable to both the dog and cat.
If, however, dogs are not acclimated to cats as puppies and are either introduced as adults into cat containing households, or a cat or kitten is introduced into the dog's household, the dog may consider the cat as prey. Sometimes the dog will attack the cat and injure it. Much more frequently though, the dog will chase the cat. The cat then spends much of its time hiding and avoiding the dog.
Consequently, the cat may avoid using the litter box because it has to go past the dog to get to the box, and it will find other areas to urinate and defecate that it perceives are safer. In addition, these cats may hold their urine and stool for long periods of time and consequently are more susceptible to cystitis and constipation which also contribute to litter box problems.
To address these issues, make sure that there are multiple litter box stations so the cat does not have to go near or past the dog to reach the litter boxes. In addition, if necessary, put additional feeding stations out where the dog is unable to reach the cat food. Cat food is very palatable to dogs, and nervous cats may not eat sufficient quantities or drink enough water if they have to compete with the dog for access.