I've fostered over 100 cats in the past 13 years and have seen this many times. Since you've ruled out UTI, here's what you have left to determine:
- stress (loss of job, death, forclosure, new family member (baby or pet), move (you said new house, just how new?), anxiety from the dog rubbing off on her?
- she's offended by the litter (odor, texture, cleanliness), style of box (most do great with the plain old shallow litter pan - without the cover), or location of the litterbox (must be in a quiet, secluded area, and away from food/water. Consider using a litter called "cat attract" for a few months. This litter has been treated to attract cats to use it for their bathroom needs.
- there have been occasions where new materials have been treated with an ammonia based chemical (I've seen it plenty of times in new carpets and leather).
Ideas for helping with stress: Pheremone spray/diffuser/collar by Feliway (and there are a few others out there now too). These pheremone products (almost like a body odor or hormone odor for cats) that mimics the scent a cat leaves behind when they rub their face/cheeks/whiskers on you. This is "marking" their territory to say "you are mine" or "I accept you as my family". First, your cat will feel less "mischeivious" when this pheremone is used. If you have trouble areas that are "stained" regularly, the spray is the best product for the job (right after a good enzyme cleaner). The next time your cat goes to inappropriately urinate on the offended spot, he will first smell the area and get a "whiff" of the Feliway and makes him think "hm, another cat has rubbed his face here . . . so this is where I am supposed to rub my face, not spray my urine". It has an overall calming/accepted effect on them.
(side note: they have a similar product, DAP for dogs that mimics the odor the mama dog gives off when puppies are nursing on her. It is often used for dogs with separation anxiety. It may help your dog feel comforted and safe).
Other things that you might consider: Give daily treatment of medication or holistic type of treatment such as Bach Flower Remedies, Flower Essences, or vet prescribed anti-anxiety medication. This is a link to a website with some solutions that target the issues your cat is exhibiting especially the treatment called "Love My Litter Box:.
http://www.catfaeries.com/essences.html . These remedies are meant to be used for several months as it often takes time for stressful reactions to go away and more tolerant behavior to become more habitual. If you don't feel comfortable with these, then see if your vet can prescribe an anti-anxiety/anti-depressant for several months to get your kitty more emotionally adapted to the stresses that are causing this behavior. And if you are groaning about the ridiculous thought of attempting to put a pill down a cat's throat, wait . . . I have something for that too! Ask your vet to write the RX for you to have filled outside of their office. Look up "compound pharmacy" in the yellow pages and take your RX script there to be filled. Ask them to make the prescription into a transdermal cream. This way you can rub the cream on the inside ear flap of the cat and it gets absorbed quickly into the bloodstream by way of the blood vessels just below the skin. So let's just say, it works similar to a nitotine patch. And if the cat is offended that there is something in his ear, let him paw it out and lick it for even more effectiveness! Feel free to PM me for any questions.