Problem 1 : The urine odor. Try saturating the smelly spots with Natures Miracle or Odoban. Let air dry (keep windows open day and night), then have the rug professionally shampooed. Chem Dry comes to mind. Good luck. Problem 2. Regarding the behavior of the Nanny. My daughter is a self-employed nanny. She has plenty of customers because she is darn good and kids love her (and she loves them) . She is reliable, always on time, will clean up a little, make meals and feed kids, changes diapers, has her own transportation (Mom and Dad keep her car running, but she buys her own gas). Anyway, my daughter would never, ever have a pet. She owns a cat that lives with us (Mom and Dad). She had an apartment for a while but her cat remained with us. So, allowing a Nanny to even have a pet is OUT. Tell your sister to be very careful in her next hire. And my daughter's in New York, and not willing to re-locate, so I guess she's out.

Having dealt with cat pee I know it's REALLY annoying and very difficult to get rid of 100%. Natures Miracle is ok, but I have found that the Natures Miracle specifically for cats is even better. Another option you might try is something called Sweet PDZ. It's used in horse stalls to keep the horse pee smell down. I use it in my back yard to keep the smell of dog pee away. I can buy a 25lb bag of it for $8 or so. It's supposed to work well on cat pee too. Here is a link that might be useful: Sweet PDZ

Joepyeweed is right. You have to give the solution a good long time to work. If you keep the area damp with the solution, it will digest the stain. I once got blueberry stains out of a white cotton shirt by keeping Simple Solution damp on it for three days. No sign it was ever stained. I have an almost-house trained dog, and another who is on steroids, so sometimes must go in the house. I first use my Spot Bot (or Little Green Machine - same difference) to suck up as much urine as I can. Then I soak the area with SS and let it sit at least a half hour and suck up the fluid (hoping to "wash out" more urine with the SS) and then I soak it again with SS and just let it dry. If it is a vomit stain or other difficult stain, I will cover the carpet with a damp cloth to make sure it does not dry too quickly. If you use any kind of machine to suck up this kind of spot, you will find that the machine soon reeks! I wish the instructions had said to rinse the machine several times before putting it away. I will suck plain water through the nozzle and hose, dump the container and repeat several times. The last time, I use it to suck up Simple Solution and then let it stay in the machine. Oh, how I wish I had done this from the start! My new game plan for dealing with incontinence is to cover the hallways (where the dogs "go") with washable quilted incontinence pads like they use underneath people in hospitals and nursing homes. I got them for my father-in-law originally, but found that they worked great for the dogs, too. They contain the urine and have a waterproof backing, so the urine does not get to my carpet anymore. My father-in-law lived with us and his caregivers were here all day. He died a couple of weeks ago and my three dogs are now alone most days. I have my sister stop by on her way home from work mid-afternoon, and she lets them out for me. On the few days that she has forgotten or my arrangements fell through, the dogs have been making it through the day pretty well. My almost-house trained girl is getting better and better. It almost seems that she is finally "getting" it!

Keep in mind that cats and dogs can smell things we can't. If there were cats living in your apartment previously, your cats may be able to smell any old urine spots, even if the carpets had been cleaned(especially if the pad or subfloor wasn't treated) or replaced. Most odor eliminators use enzymes that take time to work and as Elly_nj said, you have to soak all the way through to the floor. I have used Nature's Miracle more than any other and it has always worked for me, but at times I've had to pull up the carpet and soak the backside, pad and floor to get the job done. Also, if it's mainly a couple of problem areas, after you treat those areas, re-arrange the furniture if you have to, to keep your cats from getting to those spots. Good luck.