Just checking -- are you completely sure the cat isn't sick? Suddenly starting to pee outside the litterbox can be a sign that something "back there" is infected or impacted. I've had a cat with this problem, and after she was treated she went back to peeing in the litterbox. The litterbox is where they naturally want to go.

...though if an area smells like pee, they may still treat it as the "new litterbox." Try an enzyme spray for pet stains like Little Buddy.

Before giving up, I'd get the cat thoroughly checked by your current vet and a new vet and treat sheets with enzyme sprays before laundering (laundering may not be getting all the smell out to a cat's nose). Bedrooms might also be off limits to the cat for a while until she is back to peeing in the box only.