I see that you are now offline, so I will send your answer and then, if you have any additional questions, please click 'Reply' and I will be glad to continue.
Typically, inappropriate elimination in cats can be caused by an underlying medical problem or a behavioral issue. The best first step would be to have your cat evaluated in person by her vet and a urinalysis run, to see if there are any bladder or urethral infections present. When a cat is in pain or experiences discomfort upon urination or defecation, she will seek out other places to eliminate, avoiding the litterbox, thinking that this will eliminate the pain. UTI's (urinary tract infections) are not uncommon in cats and sometimes, if the urine isn't acidic enough, tiny crystals (sand-like particles which are sticky and have sharp edges) can form and cause pain, plus they can clump together and cause a blockage and/or stones in the bladder/urethra. There is another condition that is not an infection, but an inflammation of the bladder walls, called interstitial cystitis; this can cause similar symptoms to a UTI and is painful, but can be treated.
Right now, it is strongly recommended to have your cat evaluated in person by a vet and a urinalysis and urine culture run, in addition to a routine blood panel (CBC/Chemistry) to find if there is an underlying medical problem causing her inappropriate elimination. Here is more information for you to read: CLICK
If all is well, physically (hopefully!), then what you describe could be caused by stress. Cats don't show stress like humans do, but use other 'signals' that something is causing them anxiety and one of those signals is inappropriate elimination. If there have been any changes in the household recently, or in your routine or even the addition of the dog, these can all contribute to stress. A cat will feel the need to 'mark' territory if she feels stressed or threatened by any new changes. Even a change in your daily routine or work hours, etc., can cause this. If you haven't gotten any new furniture, changing the position of the furniture could also be stressful to a cat. In general, cats typically don't take kindly to change and may act out in this way.
Get some Feliway plug in diffusers; these emit cat-calming pheromones that help with inappropriate elimination. They resemble plug in air fresheners, but have no scent to humans, only cats can detect it. You can find Feliway in major pet supply stores, some vet offices, and online. Here is more information: FELIWAY
Make sure to clean the areas she soils, with an enzyme-based product to remove organic/pet stains. This is the only type of cleanser that will completely remove the scent so she doesn't continue to smell it and eliminate there again. Some well-recommended ones are Nature's Miracle, Zero Odor and Odor Mute; these and many others are available in pet supply stores and sometimes, in Walmart, Target, etc.
Also, after you clean these areas, allow to dry completely, then lightly spray some Feliway and allow that to dry completely, as well (about 30 min.) before allowing the cats access to the areas. This will make her think she's already 'marked' there.
If you're now using covered boxes, try uncovered, or have half and half; some cats prefer one type and others, the alternative. Add a kitty litter attractant called Cat Attract, to all boxes and make sure they are spread out around the house in different locations. Cat Attract contains herbal attractants that encourage use of the litterbox and you can buy it in any major pet supply store. Here is more information: CLICK
Also, make sure she's not bored and enrich her environment with some interactive toys and toys she can play with on her own. Here is a great list:http://www.catdvd.com/http://www.frolicat.com/http://www.batarat.com/ http://www.pawswhiskersandclaws.com/pwc%20foraging.pdf
If you don't already have one, get a kitty condo or cat tree with multiple levels, shelves and 'hidey' holes. These are great for scratching (they're covered with carpet), playing, and also sleeping. If you have room for two, the cats will love them!
I hope all will be well with your furry girl and things will improve soon. Please make sure to get her seen by her vet, to rule out any underlying medical issues.
Please kindly rate my answer with positive feedback and if you have any additional questions, just click Reply and I will always be here for you and your kitty. Rating will not cut off our ability to communicate. This question will always be open for you to reply to me.