Dog eliminating near litterbox

Question
I have a nine year old dog in stellar health, she just came back from her routine checkup last month. She's always been on the nervous side, due to being taken away from her mother too early. (We adopted her as her second owners, because the first owners couldn't take care of her. She came to us at 7 weeks old, crawling with fleas and a total mess.)

But within the last two years, we've gotten two cats. The first cat came to us in 2013, and initially the dog seemed fine with her. She ignored her. When the cat started getting older, the dog started peeing and pooping in the corner of the house with the cat's litter box. At first we thought it was the cat, because we'd never really trained her to use the litter box, but some months later a house guest managed to catch the dog in the act. We've never caught her doing it ourselves, she always does this when there's no one around to yell at her. It seems willful, like she knows she isn't supposed to go there.

I got my second cat in December of last year and it's become clear that the dog is eliminating where the litter boxes are. I need to break her of this habit, and fast, because the house has all wood floors and the ammonia has begun to stain them. The trouble is, I cannot move the litterbox. We have an open floor plan and there's nowhere that we can isolate from the dog without also isolating it from the cats. I've tried erasing the scent markers, I've tried blockading the general area (the cats knock down the baby gates and it becomes moot)... We have a whole litany of cleaners dedicated to this task.

My dog was always extremely well behaved before. How can I modify her behavior if I can't catch her doing it?

Answer
Kaden, the solution to this isn't training. It's simply management. Find a gate the cats can't knock over. There are plenty of them. There are also gates that have an opening for a cat to fit through.

You should also crate the dog when you are away from the house so she doesn't begin marking in other areas.

I also might recommend an over-the-counter calming remedy containing l-theanine to reduce her overall anxiety of having another cat in the house.