Hi, it could be that your cat has a urinary tract infection such as cystitis - especially if you say she is drinking lots of water too. They use their tray normally but if they feel sudden pain from an infection they will just do it wherever they are to relieve the pain. It could also be a territory marking thing as you say - especially if you have another cat in the house. It's important never to punish them (frustrating tho it is - I've had similar problems for a few years) as this will make the cat insecure and more likely to mark the territory. Have a look at some of the cat websites such as Cats Protection or Feline Advisory Bureau as they have advice leaflets on various problems. I'd definitely take her to the vets for a check over tho - antibiotics for UTIs are dirt cheap in my experience. Good luck.