The most common reason for litterbox problems are surface and location preferences combined with a litterbox aversion. I suspect your cat does not like her litterbox for any number of reasons - not clean enough, location she doesn't like (too hard to get to , too noisy, etc.) covered (or not), litter not soft enough, litter too deep, been "ambushed" in the box, etc. etc. Tom made some good suggestions but the more we can decipher why your cat isn't using the box the more likely the recommendations will be to the reason for the problem. You may best be served with a private behavior consultation.
try comparing the places she does soil to the litterbox and its location. How are they different? How are the soiled locations meeting her behavioral needs and the litterbox isn't? How can you make the litterbox and its location more like the soiled areas?
I'd also suggest reading Cats Come Clean: what you cat wants you to know about litterboxes. You'll better understand the reasons for these problems plus find many suggestions about what to do. Go to
http://helpingkitty.com/booklets-cats-come-clean.htm
Your cat's behavior has nothing to do with how much attention she gets or being "jealous" of your other cat.
Most litter box problems can be resolved so don't give up on your kitty, but a good physical by your veterinarian is a great first step
Part of the joy of owning cats is the fact that you can have several of them concurrently and they don't seem to run into the same issues as large dog "families". :-)
Until recently, my household consisted of a minimum of three cats at a time, often I would have up to 9 or 10! I have run into the same problem that you are describing with older cats on a couple of occasions.
First, how many litterboxes do you have? If you just have the two cats, you really need to have three litterboxes (one per cat, plus one). Next, the placement of the litterboxes can be important as well. Your older girl could very well be suffering from arthritis (although it is hard to tell with cats because they mask their pain so well) and moving around the house could be difficult. Consider making sure that litterboxes are available on EVERY level of the home that the kitty has access to. Also, litterboxes placed in noisy areas (busy laundry room, room with dog kennel, etc) can be a hinderance to the cat because they would like to have some privacy.
Second, has she been in to your veterinarian recently? The very first step with any inappropriate elimination habits is to do a complete physical with potential bloodwork and urinalysis. She may have a medical condition that makes it difficult for her to urinate or defecate.
Finally, whatever the underlying reason is (behaviorial or medical), wherever she has eliminated in the house must be cleaned with a pet enzymatic stain and odor remover. Products like Nature's Miracle work wonders to help remove the odor and thus the attraction to continue to go on that spot. It may take several treatments to fully remove the odor and you might even need to block her from accessing that area for several days.
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I hope this answer helps you...please make sure she gets a good physical by your DVM and then go get some stain/odor remover to help lessen her attraction to go in the same places. Good luck!!
This is so difficult to live with, I know since I had a similar problem but not as bad. First I got rid of anything that cat had soiled and then got her own litter box and put it in a very private location and kept it immaculate. She was happy and so was I. Good luck