Welcome to the forum, Melissa. Know that this issue is the #1 complaint of cat owners. You can spend time googling this and see all the solutions for other people. But, you need to make sure there is not a urinary tract infection going on or crystals in the urine that can be painful when she pees and she associates that pain with going in the litter box.
If you have had your cat checked out by a vet and there are no health issues, then this becomes behavioral. You say she uses the litter box. Since she is using the carpet, this does appear to be peeing rather than spraying. My suggestion is to add more litter boxes. Especially in the area is she using. The type of litter box and the type of litter can contribute to not wanting to use a certain litter box.
As for cleaning the carpet -- yes, you're getting the carpet clean, but the padding and subfloor underneath has been saturated and that smell is NOT going to go away until everything has been pulled up, thrown out and any subfloor primed with a sealer on the stain (concrete or wood). And a cat will go back to that same location over and over again as long as the odor is still there. If you can smell it, it is quite pungent to the cat.
Now, another issue. You said you were gone all weekend. I guess you left your kitty home alone? Many cats can suffer from separation anxiety. Your kitty was probably bored to death while you were gone with no human interaction.
It is always best to keep your kitty indoors. They somehow have no idea of the dangers that lurk for them in the outdoor world. I read every day of cats being hit by cars and laying dead on the side of the road. And, cats have their own ideas of where they want to go and it's not where you want them to go. You can always try training your kitty to walk on a harness and leash (which is what I've done and my bengal gets two walks a day).
I will reiterate that you may need to add a couple more litter boxes. If you see she is about to pee somewhere else, pick her up and put her IN the litter box. This issue will not solve itself without some intervention from you. I know how frustrating this is for you, but this is not your kitty's fault. They are usually trying to tell you something isn't quite right and you just have to figure out what that is. Good luck.
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