My Boy does the same, he suffers with IBD, he seems to do it more when he has his bad IBD pain, my vet said cats poo is like caviar to a dog, cats food is higher in meat protein & dogs can smell the meat, I had to teach Patch the words "LEAVE IT" & spray him with a water spray bottle if I caught him, this has helped but my cat started to poo outside since we moved & this is a nightmare I have to find where she poos before he finds the cats poo, your situation is easy cause your cat poos inside. Cats like to jump up & be high, put her litter tray up high on a table or bench top etc so the dog can't jump up onto table etc also what I did was get a kitty litter that has a lid & the cat has to push thru a flap to enter her kitty litter, but it sounds like your dog would just push her head into the Kitty litter.
Start you're dog on a good dog probiotic so her gut gets healthy again, best to give probiotics in between meals or 1st thing of a morning when stomach is empty & stomach acids are low, not high like they're when they eat, I was giving Patch probiotic powder mixed with10mls water & he'd drink it from the bowl at 11am daily given as a treat, he loved it..
Purina Forti Flora probiotic came 1st when 20 dog probiotic were tested only 3 came back with live cultures, the rest were a waste of money, so becareful & do your research, another good brand is "Adored Beast- Love Bugs"
also give your dog a meaty chicken wing, chicken drumstick or a chicken Carcass, something she can chew on & loves more then the cat poos are a treat, the meaty bones will clean her teeth & the probiotic will make that bad smell that's coming up from her stomach once her gut is healthy again.
Good-luck