I'm sorry that your question wasn't answered in a timely manner. I have advanced training in feline behavior and am pleased to discuss Mrs. Black's behavior with you. I must admit that retraining her is going to be a challenge but perhaps after reviewing my notes that I use when lecturing about her behavior you'll have a better idea of how to address it.
Mrs. Black is clearly exhibiting marking behavior. She is not likely to be eliminating inappropriately due to litterbox aversion or a medical disorder - which appears to have been ruled out by her vet. Marking on a horizontal surface (the cupboard, e.g.) is marking behavior (a communicative function) caused by the same stimuli that causes spraying. We’re not sure what cats are trying to communicate to us but we do know that wild cats will mark to announce their presence. It’s reasonable to assume then, that Mrs. Black is doing so as well. She’s essentially “taking ownership” over marked areas which then assuages her anxiety. The most common cause is increased cat density - in the home or nearby. Emotional problems, such as a stressful relationship with a family member, separation anxiety, anxiety over her status in the existing hierarchy/your granddaughters, fear, owner absence, moving, new furniture, inappropriate punishment, teasing, household changes and remodeling in the home are examples of stimuli that can induce anxiety in our cats. The etiology can be difficult to diagnose, especially if the behavior is only manifested intermittently and because the stimuli for her inappropriate eliminative behavior may be imperceptible to you but readily so to her - another cat roaming outside, e.g. If emotional factors are influencing the housesoiling, you might notice other changes such as avoidance, aggression or an alteration in her general temperament.
Treatment involves two major considerations: 1) Remove the cause - easier said than done. You might have to be quite the detective to discern the stimuli for her inappropriate eliminative behavior 2) Prevent Mrs. Black from returning to previously soiled areas by confining her to a very small area with the box and only allowed out when she can be supervised 100% of the time. When confined to a relatively small area, most cats seem to prefer to eliminate in the box rather than soiling the floor. It’s then a matter of confining her long enough for a consistent habit to become established. As a rule of thumb, one week of confinement is usually recommended for every month of soiling. She should be removed from the confinement area as much as possible for socialization and play, but never allowed out of sight. Food rewards may help when given after she uses her box. If she refuses to use the litterbox when confined to a small area, the confinement area should be changed to a large cage. The floor should be covered with litter, forcing her to use it for elimination. The litter is gradually removed and replaced with a litterbox. Once she has used the litterbox in a confined area for an appropriate amount of time, she can be allowed to have more freedom in the home. Previously soiled areas can be safeguarded by changing the behavioral function of the area by placing food bowls, cat bedding or toys in the area. The area can also be made unacceptable for her by placing a motion-activated alarm or lemon-scented room deodorant in the area. Plastic carpet runners can be placed upside down with the "feet" facing up. Plastic, foil, or double-stick carpet tape can be used to protect specific areas. Removing urine and stool odor is important. Products such as Nature's Miracle which are specifically formulated to work on these types of odors are recommended.
Some cats are extremely sensitive to changes in their environment. They may mark in response to the most minor of alterations. You must strive to keep the home environment as constant as possible. When situations exist that are likely to upset Mrs. Black, you might want to consider confinement, closer supervision and the use of anxiolytic (anti-anxiety) medication such as paroxetine (Paxil) and fluoxetine (Prozac). In fact, most behaviorists feel that without the use of psychotherapeutic drugs our chance of correcting inappropriate marking behavior is near nil. (Personal note: My two cats began marking as kittens. After 6 months of fruitless treatment they became outdoor cats - for 12 years.)
Nobody wants to confine their pet as I've described but her behavior requires desperate measures. My male urinated on my pillow while I slept - an obvious behavior designed to make sure that his sister and I knew who's bed it really was. He apparently was anxious about his status in the hierarchy of my home.
Success in management with psychotherapeutic drugs is measured by a 70% reduction in adverse events. In other words, if my cat urinated on my pillow 10 times monthly prior to drug administration but only 3 times monthly after drug administration, success in treatment is acknowledged. Needless to say, that didn't please me and I certainly hope that you have better "success" than I. Perhaps you will not having another cat in the house.
Please respond with further questions or concerns if you wish.