Nature's Miracle works great. Just as a warning though...it will smell worse when first you pour it on the pee spot. Wet pee stinks more. It will then smell even worse than that over the next day or so while the bacteria eats the pee, I've read that the smell is a by-product of the bacteria's digestive process. After about 4 days there will be no smell at all, not even a soapy smell. There may be a stain that remains, give it a week to completely dry then clean the carpet like your would for any regular stain.
Pour it on and let it sit. Do not try to suck out the moisture from the Nature's Miracle, it needs to stay wet for at least a day or more. The bacteria can move around better in the wetness. Don't rub it in and don't just dab it on. Pour it so that every portion that may have been peed on is wet and then leave it alone.
I've treated pet pee sports with Nature's Miracle many, many times. Don't worry about mold, I've never had any occur during the treatment. I think maybe the bacteria prevents it...I'm not sure why, but it's never been an issue for me.
Since you are treating an area rug, you might want to limit how wet the wood floor underneath gets. I would probably pull back the rug and just rub the wood floor underneath with a rag that has the Nature's Miracle on it, let it dry for a day, then maybe the next day cover the wood with plastic while you treat the rug on top. I wouldn't want my wood floor to be wet for several days. If your wood floor is sealed, it may not smell at all. The poly does a great job at protecting it.
Another important point with Nature's Miracle, don't buy a huge bottle just to keep it on hand, only buy as much as you think you need. The bacteria in the bottle will die after a while and an old bottle won't work.
Good luck! (I know wayyyyy to much about how to clean up pet pee)!