What To Do With a Cat That Pees in the House?

One of our cats, Patches, seems to be peeing in the house, not in the litter box. I say seems, though there really is little doubt of it. At christmas when we brought a couple of chairs in for Christmas dinner so family would have somewhere to sit the second we brought them in she jumped up on one of them and peed on it, in front of several people. Every once and a while, but getting more frequent it seems, she goes somewhere in the house. There doesn't seem to be any real rhyme or reason to it. Just randomly around. And it's a big enough house that we don't always see/smell it right away. Sometimes it's just things on the floor, ie: a plastic bag just dropped in the middle of the floor, or a work glove left in a corner. This evening when I was turning out the lights to go to bed I was down at the front enterance and was hit by the now familiar horrible smell of cat urine.

No source of course. I spent about five minutes wandering around the basement and front enterance, periodically getting down on hands and knees to sniff a suspicious stain on the floor, or a glove, or a bit of leftover insulation. The only thing I found was a relatively old pee spot on a plastic bag full of drywall screws sitting on a workbench. Dead center.

No rhyme or reason. She was doing it in the heating vents at one time, other times on the (old) couch (pretty sure of that anyway), and a couple of times my backpack, which was thurouly washed after the first time, but was smelling again when we got back from holidays and it was left on the kitchen counter.

I don't know if it's a territory thing (the new chair incident suggests this) or a bladder infection (she's been checked by a vet, bye bye another $500 for that thankyouverymuch) or a stress thing (construction around the house, but she's been doing it for longer than that) or something to do with abandonment issues. Hell, I don't even know if it's new to this house or if she was doing it at the apartment when we first got her. Maybe that's why she was abandonded by her previous owners.

She uses the litter box fine, we've seen her use it. We've taken her to the vet like I said and he said she had a mild bladder infection and we nuked that with antibiotics. We have gobs of litter boxes which are cleaned regularily. We clean any spots we find thoroughly, but of course, sometimes we don't find them for a while.

I'm pretty much at the end of my rope. I'm sick of not wanting to have people over because my house smells like cat pee. I'm sick of having to worry that if I leave my bag on the floor I have to stick my nose in it to check to make sure it's still ok. I'm sick of catching the hint of something and not knowing if it's pee or not, or if I'm imagining it or not.

And I don't know what to do. Realistically I have two options.

• Keep cat.
  
• Don't keep cat.

And from that it comes down to something like

• Keep cat and accept that there'll probably be more peeing in the house. Maybe it'll end or slow when the basement is done, maybe not.
  
• Send cat to the SPCA for adoption. Maybe the issue is the multi-cat home. She isn't particularily friendly with the other cats, but she's not a loaner by any means. Her and Zoon will play or groom each other. Maybe whoever gets her won't have any issues at all. On the other hand, maybe I'll just be foisting the same problem on some other unsuspecting person or family.
  
• Put the cat down. Most definately will make the problem go away, and also the hardest choice. I've never put a cat down before and obviously would rather not do this to someone under my roof. If it's a choice of this or having a house that smells like cat pee for the rest of my life though...
  

Any other options? There are some webpages on stuff like this, like this one, with a lot of suggestions that are already done or are good ideas and may not work for me (ie: putting peed on items in the litter box is a fine idea, how exactly to I get my furnace vents in there though? ).

So what do I do to save my house and my sanity?