[sugarcatmom]

Have you tried setting up 2 or even 3 litter boxes? Especially since you have 2 cats, it might be a good idea. For sure you'll want to rule out any urinary tract related issues, so if she hasn't had a vet check-up recently that would be the place to start.

Stress can be a factor with inappropriate elimination. How well does she get along with the other cat? Even if there are no overt signs of hostility, it's possible that there are underlying subtle territory issues between them. Putting another litter box in a different area of the house can help, as can increasing the amount of vertical space that the cats can claim (like with a cat condo or shelving or window hammocks, etc).

I'd also suggest trying a couple of Feliway diffusers if you haven't already. This can sometimes help with stress (like from her wanting to go outside) or if it's a territory thing.

The other thing that could be at the route of this might have to do with the furniture itself. You say you bought them used, so it's entirely possible that they were "marked" by cats previously, and she's just doing her due dilligence by re-marking them. Even if they weren't actually peed on before, they would have had strange scents from their previous owner, and some cats are strongly compelled to mark over-top of a new smell in order to make it familiar to them. Any way you can remove the furniture from your house entirely and see what happens?