How exciting! Caesar never had training problems, but Beta was a wreck. She was an angel the first 6 months and then she began peeing in any room that i wasnt in. At the time i had a townhome where the bedrooms were all upstairs. I had the stairs gated and my basenjis had full roaming of the living room dining room and the kitchen which was visually blocked by the kitchen countertop from the living area.
Once Beta hit 6 months she began changing or adjusting to the home and the other animals (Caesar and the 4 cats). She became snarfy, she became food aggressive, and she started to sneak out of my sight to pee on the kitchen floor or in Caesar's bed.
The downstairs wasnt huge, so I didnt understand that the area was too big for her. In her case, she was asserting herself as alpha to the other pets in the house. Beta had a very difficult life before I adopted her and it took me 2 years to finally teach her that you pee only on grass. I am not saying that your pup is pooping for the same alpha reason, but here is what I had to do to get her to stop.
I was so frustrated and knew that she was no where near ready for basic training. I knew she was adjusting. I understood that what she was doing was behavioral not physical.
I brought in a trainer who becan to work with her because I was out of ideas. He suggested that the area she had to roam in was too large even though it seemed incredibly small to me. He told me to keep her harness and leash on inside the house. This made Beta aware that I was on top of her. If she went into the kitchen, I was there holding the leash. If she was in the living room sitting, I was there. Sometimes I just attached the leash to my pants to make it easier. She never peed in front of me and basically stopped the behavior because I was with her.
The other major thing I found that helped Beta with settling down was exercise. She required a lot more exercise than Caesar. When I moved to a place with a fenced yard or took her to the dog park she could just burn that energy off.
I found with Beta, that treat training would just not work for her. She would get extremely excited about treats, but her behavioral problems were mostly affected by my actions and attention. Food didnt matter.
Caesar was really easy with training because I adopted him as a puppy. I could use the crate for time outs and he understood and would improve.
Beta lived in a cage for over 1year and a half straight which was too small and in her own filth. I couldnt and wouldnt use the crate as time out for her. She liked going to the crate, and going to the bathroom in her crate was easier for her because it was her environment for so long. Her problem was adjusting to the world outside.
So, restrict the area and keep a leash on her. She may be getting too much free roaming space too soon. Can't hurt to try it. She will soon forget what she was doing.
And dont forget to get that Natural's Magic (I think that is the name) for pet smells in the carpet at your pet store. This should keep her from revisiting the same spot if she is doing that.
wouldn't you NOT speed 
well same idea with dogs.
