As you're likely well aware, the reason that I asked about the urinalysis and the fecal exam were to rule out medical problems. If this is a medical issues, and it sounds like that has been ruled out, we have to assume that it's behavioral. Here are some steps that may help her:
1) Make sure that she has a private area that she can go while she's outside. If possible, this should be out of the way (such as beside a building) where she can go safely without concern of being disturbed. If she is leash walked outside, such as living inside of a condo or similar, you will have more concerns with this because of the open nature and inability to allow a dog off leash to potty.
Dogs are much more in tune with their environment than we are and this is especially the case of an anxious, nervous or scared dog. They will be hyperaware of what is going on around them. If there is any change in traffic patterns, increased noise, other animals, children, adults, etc. this can all affect how comfortable they feel when they go outside to potty. Many owners who battle this type of issue will log when their dog is having an accident and can track the dates to see if they correlate with anything concerning like the trash man coming, meter reading, etc.
2) Remove all privileges to the house until she has earned them.
One of the biggest mistakes we can make with a dog that we wish to trust, but cannot yet trust, is to give them too much space too soon. As she has already shown you, her "area" (kennel) is not somewhere she wants to potty. Until she realizes that your expectations have expanded do the general home, she's going to continue to use it as an area that she can soil. Slow, steady introduction of more space should help her to slowly widen her "den" territory and view it as her home. For the time being, her kennel is this area and perhaps slightly wider area but the bedrooms certainly don't count.
For this, try starting with just the room that her kennel is in. Most dogs tend to be left in the living room, so this type of area should come first. Block off all adjacent and adjoining rooms so that she does not have access. Since you're seeing a few accidents every few days, go about a week before adding more space to her area. Start with an extra room, like the kitchen, and slowly add more and more space until she is not having accidents. If she does have an accident, go back to the week prior's space and give her an additional week. Then, move back up to giving her access to the area again.
3) Consider having a behaviorist come to your house to evaluate her outside to see if there is anything that they can see about her behavior that would suggest that she has direct purpose for wanting to avoid this area for pottying at least part of the time. Sometimes a fresh set of eyes on a situation, especially in the home, can help greatly.
4) Talk to your veterinarian about placing her on a low dose of behavioral medication to lower her inhibition to go potty outside while stressed. The idea here being that she gets into a routine on the medication and you can then wean her off of the medication and the positive behaviors remain.
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