Aww poor kitty (and you). It's just a rough situation all around. I love my mom dearly, but if circumstances were such that I had to live in her house and give up mine, I think I'd be feeling a bit territorial and stressed myself! I wouldnt pee on her carpet, but I would sure understand why my cat might!

Have you used feliway - if not get a plug-in asap. Does not always work but does often enough to make it worth a try.

You may not know, but are you thinking this would be a short term situation or is it likely to take a while?

Was her vet visit before or after the move?

So often stress suppresses the immune system & a real, actual medical problem develops.

If I were in your boots & I were going to buy another house within the foreseeable future, I'd hang in there;
I'd keep my cat, plug in the feliways, maybe get the vet to put her on valium or prozac, & replace the carpet & bedding after I moved out.

I wish you the best.

If you truly want to find her a new home, contact your local rescue groups. If she's healthy, a Siamese cat shouldn't have problems finding a new home. I don't think it's fair to even consider putting her down since she only reacting to the stress of another cat, new home & location, being locked in a basement and then locked in the bedroom. Plus, she probably doesn't see you as much as she used to.
On top of all that, she now has the additional stress of your response to her accidents.

If you really want to keep her and intend to move as soon as you find a place, then I'd suggest finding a pet boarding facility that houses only cats. My local Cat Clinic boards cats......and they each get a nice room with a large viewing window. I think it'll be less costly in the long run.

Take her to the vet for urinalysis. This is a common symptom for urinary tract infection.