Aww, you are doing such a nice thing for this doggie--taking her in so she doesn't have to go to a boarding facility. I am one of those people that could never enjoy a vacation if my dog was in a kennel, and I am super grateful that we have a neighbor that loves to watch her. As for the dog not being trained, it is possible that she doesn't behave like this at home, so maybe the owners really did think it would not be an issue.
My dog (a mini poodle) has been trained for years, but if I dropped her off at a completely unfamiliar location, I can't guarantee she wouldn't have an accident out of fear or nervousness. She never has accidents at our normal dog sitter's house, but who knows what would happen in a totally strange environment? Also, maybe the dog you are watching has some sort of medical problem contributing to her accidents? Hard to know for sure, but you are doing the right thing by keeping her (and not dropping her at a kennel) in spite of all the work she is causing. Try to enjoy her sweetness, and the way she plays with your dog (I think you said your dog enjoys her). You are a good person!! I bet the owners give you a nice gift card when they return!