I agree that a trip to the vet could rule out anything medical, even though it does sound like a “trauma of moving” sort of thing.
The one room plan is probably a good one, although I know that some apartments don’t really have one room that can contain a pet, short of the bedrooms. Cats are very fussy about their litter box, there could be some crazy reason why she doesn’t like the location of the box now. You might try putting down several litter boxes in a few different places, and see if she takes to any of those better. Does she go in her box at all, or just to poop, or never?
A gross question, but here goes – is your dog the kind that wants to check out the cat’s box? This can be very off-putting for cats. It might also bother the cat if she feels the box is kept too close to her food and water, or if it is in a high traffic area (by the cat’s own standards, it could seem completely out of the way for you). If her owner says “oh, but we kept the box in the hall in our last apartment, and she was fine,” well, it just doesn’t matter to a cat. That was then and this is now.
More for furniture, but I assume it would work on floors, too, is double-sided tape. Most cats will not like having their paws touch the sticky tape, so you could try putting down tape in such a way that it would form a barrier around the area where she is currently peeing. Of course, this is only temporary, because you do not want tape on the floors of your apartment forever, but it might be enough to break the cat’s habit after a week or so. Obviously, it has to be enough tape that she can’t simply walk or jump over it. This might not be an option depending on the size of the problem area, but maybe it would work in a doorway to keep the cat out of the dining room altogether.
I know you’re cleaning up each time the cat pees, but scour the area in the dining room. It’s possible that a previous resident in your apartment had a cat, and if your current cat can smell any trace of old cat pee, that sends a message to her that this is the place to pee. For all you know, this is where the previous resident kept the cat box. If there’s just something about the dining room that she likes, you might put her litter box close to where she is peeing now, and see if she will then use the box exclusively. Once she is doing that, you can gradually move the box closer and closer to the area where you actually want to keep it.
Whatever you decide to do, do it quick, because cats form very strong habits about where they pee. There’s a product called “No Go” that you can get at petstores for cleaning the accident spot that supposedly makes the area smell unattractive to the cat in the future. I haven’t used this myself, but someone at work found it helpful.