First things first--train the dog to do her business outside, not in the house! Don't do anything else until she learns what the outside is for. Since she now thinks her behavior is acceptable, it will be a challenge to house-break her. I'd suggest a confinement cage, as most dogs won't soil the area they have to sit or lay in.
There's a commercial, microbacterial product available that does wonders for the stench of dog pee. Can't remember the name, but it's available where motels and hotels get their cleaning supplies. Did wonders for the last place we lived in, where the previous owner had allowed their Fido free run of the house, all day long, no one home (flooring actually rotted out under the carpet at the door to the back yard, poor dog).
Since you've already changed furnace filters, I suspect your next option is to have all of the ducts cleaned and sanitized (after potty training, of course).