Thanks for answering my questions.
If someone were to ask me the primary negative trait of small dogs, difficulty in house-training would top that list (and I speak from experience since I am currently owned by a Maltipoo). Part of the problem is that tiny dogs physically just can't hold their bladders for as long as bigger dogs, but often the issue is that the owners (myself included) don't insist on house-training as rigorously as they would have with a large dog. Some people with toy breeds worry about putting their pets out in the cold or wet weather or may dismiss their messes as minor lapses and over look them. But small piddles and poops add up to a big problem that needs to be corrected, and all dogs need to learn that their bathroom is outside.
The first thing that needs to be done is for the pup to have a quick trip to the vet to make sure that she doesn't have a medical condition that is causing her to have weak bladders such as a urinary tract infection. Most likely, however, they urinate or defecate indoors because they don't know the difference or they are marking their own territory within the house with their signature scents. Both male and female dogs will display marking behavior, especially if they have not been neutered or spayed.
If this were me, I'd start from the beginning and completely retrain the dog to solve this problem. I would establish a routine in which the dog is ushered outside as soon as she wakes up in the morning, after meals, after playtime, and before bed. I would praise the dog every time she does her business outside. If you catch the dog in the act inside, you can clap your hands loudly to startle and distract her long enough to grab her and take her outside. The minute she goes to the bathroom outside, give lots of praise and a treat.
Accidents will happen during the retraining process, but it's important to not become angry or frustrated. When you vent these types of emotions, training stops and your dog becomes fearful or confused. It's also futile and silly to punish the dog when she makes puddles or defecates in the house. All she'll learn to do is to do her business secretly or when the owner isn't around to catch her.
Another step I'd take is to completely and thoroughly clean all the carpeting with an enzyme based product that destroys the protein molecules in urine and feces rather than just covering the smell up. There are many cleanup products on the market that work this way..just make sure to not pick a product that contains ammonia, since it smells enough like urine to actually attract the dogs back to the scenes of their crimes.
I know it's frustrating to get a rescue dog house-trained (it took me about 6 months to get my rescue mutt re-house-trained)...but with a great deal of consistency and patience, you can get it done!
I hope this helps.