Hi,
Okay, forgive me in advance if I repeat anything that anyone else has already suggested, because I didn't have time to read down thru the posts. I wanted to offer some info tho, because I rescue cats - I'm currently taking care of more than 30 (although, thankfully, not all are indoors!).
First off, please take your kitty to the vet because typically if they go outside of the litter box, it means they are ill. Your kitty could have a very serious urinary tract infection or kidney stones which won't go away without antibiotics and possibly an anti-inflammatory shot. You may also have to change kitty's food, and reconfigure where your kitty's litter pan is.
Can the dog get to the litter box? If kitty feels cornered at all, he/she may avoid that area and go to a "safer" place to eliminate wastes. All litter boxes need an avenue of approach, and an alternate route that can be used as an escape - so for example, if your cat's litter pan is in a closet for example, with only one way in and out, she may feel trapped using it.
Another thing that could be causing a problem is, the litter box is dirty. Do you sift it every day? I have 10 boxes in my house in various rooms and they are sifted 2X a day, EVERY day. (And no, my house doesn't smell! I know some people fill a pan with litter and don't touch it again until the cat's waste is spilling over the top...they are lucky that a cat continues to go to the box because they are very clean animals - and their sense of smell is a great deal stronger than ours. If you can't sift it every day, consider getting an automatic box. You'll still have to deal with the clumps, but not as often.)
As for the "odor" - what is the floor surface in your workout room? if it's concrete, clean the floor surface very well, and when it dries, you can seal the floor with certain paints or sealers that will basically "seal" the odor into the concrete (because trust me - you will never get it out by just scrubbing it. it's too porous). To clean the floor I highly recommend that you first clean the surface with scrub water that contains dawn dishwashing detergent, followed by a product you can buy at Walmart called "OUT". It comes in two forms at our walmart; one is a pleasant clean scent, the other is a lemongrass scent. Both are very fresh and clean and contain enzymes that help to break down the components of the urine and kill the odor.
If the effected area is on carpet, you can still use the OUT. I have actually put it into my scrubber where the water would go. It's important to saturate the carpet into the padding. Ultimately you may have to have carpet taken up though.
In the mean time, you may consider putting a litter box in your work out room - if this isn't an option, place a bowl of food over the area where your cat has peed. They don't eat where they excrete (hee). But this may not eliminate your problem- she may just go somewhere else.
Definitely check with your vet first because a UTI will progress to death if not treated....and in the mean time, she will end up going in many more unorthodox places - driving you to the brink of insanity!
If you have more questions, feel free to email me any time!
:7 Good LUCK!
PS. Don't give up on your kitty tho. If you take her to the shelter, no one will want her if she's peeing in their house. You're better off letter her go outside - even tho she's declawed they can learn to use their back claws for defense. It's a better alternative than death at a kill shelter, or being at a house where people may be mean to her for peeing, or worse - abandon her.