How old is your pup? House training sometimes takes awhile, and LOTS of consistency and PATIENCE! Please, don't give up on her over this.
Now, as far as the cat poo eating - I can totally empathize with the frustration! We don't even have cats, but the ferrell cats in the area seem to think my backyard is a litter box. I can't even let Abigail out, because if there is any within her reach, she finds it and scarfs it down.
EEEWWWWWWWWWW!!! Last time, I went in after it, scooping it out of her mouth. I always have to be ready to bathe her and - yes - I wash her mouth out with dog shampoo. It IS disgusting, and it CAN make them ill. Cat poo can be toxic to small dogs. And, no one seems to know why some of our furbabies love it, so.
I agree that the self-cleaning litter box should help a great deal - I think that's a grand idea for anyone with dogs who take a liking to cat poo. It should take a lot of daily stress from your life, and protect the pooch.