Why does my female cat urinate on my bathroom rugs?

The first thing to do is to have your cat checked by the vet to rule out any medical problems. There are new products on the market that remove pet odors and they have been effective. One I've used is from Rembo Labs called Odor Neutralizer and Eliminator. You can also try having separate litter boxes for the cats and even placing them in different locations. Another option is to use a different type of litter as that may be the problem. Also, try to keep the litter box as  clean as possible. Hope this helps.