My kitty ending up having some kind of behavioral issue several months ago. Would pee in her box but not poop there.

She loved my scatter rugs and I was going crazy

trying to figure out what was going on with her. No medical issues and the vet suggested I take her to a kitty shrink. I love my cat beyond words but I was not taking her to a shrink. I found this litter on line and it works like magic. She used the box the first day I bought it and although it is a little expensive, it is well worth the price. I swear by it.
Maybe it will help if you try it.
http://www.preciouscat.com/precious-attract-p-5.html