I agree that this sounds like a UTI (the tests aren't terribly expensive to have this diagnosed - the test itself shouldn't even cost $100, much less $600!) which is easily treated with antibiotics. If that test comes back negative, then you might need to look into various behavioral modification techniques. 10 years old is just the very beginning of the senior years for a cat, and it is unlikely that her bladder is failing her, so your first trip needs to be to the vet or you probably won't be able to solve this problem.
Second, what are you using to clean the carpet? You must use a cleaned specifically designed for CAT urine or the cat will keep coming back. I recommend Nature's Miracle (you can find it at Petsmart) or if you need something stronger, Anti-Ickypoo (no, I'm not kidding, that's what it's called, you can find it online) and baking soda.
Thirdly, place an UNCOVERED litterbox on the spot where she is peeing. Does she intentionally avoid it? If so, you probably have a health problem on your hands. If she uses that litterbox just fine but finds another place in the house to pee, I recommend that you call the Cat Behavior Hotline (you can find it here http://www.catsinternational.org/), which is an entirely free hotline to help people keep their cats when behavioral problems arise. I have used them before - usually you call, leave your name, phone number, and problem, and an expert will call you back. It really is free (although of course they accept donations, but there is no pressure) and very useful.
Finally, if this is stress from moving, a good vet will be able to give you some kitty prozac to help your cat relax. This can actually be very helpful, although it is expensive, and you can wean the cat off the drugs once the behavior disappears.
I wish you good luck. I live with a cat who urinates in the house because of behavioral issues (she was rescued from an abusive home), and I know that cat pee reeks! Ug, there is very little as gross. In the end, we had to buy a very large cat crate for her because nothing else worked and I wasn't going to give her to the shelter! Fortunately, I suspect your problem will be easier to solve. Good luck.