I think YABU to take her back to the shelter after you've had her three years. You are her family now. I am of the belief that when you take on a pet, you take them on through bad as well as good. If you aren't prepared to tackle problems your pet may have, you should not take on a pet.
I have been in a similar situation as you. When I first brought my two cats home, they did not wee and poo in their litterboxes, probably due to the stress of being rehomed. It was extremely frustrating to deal with, and made it hard to bond with them. I did quite a lot of research though, and managed to stop the behaviour by keeping them in small area of the house where there was nothing tempting to wee on for several weeks until they retrained on the litterbox. I also rewarded them everytime I saw them go in the box. Now we have no problems.
Your cat sounds like she was very stressed by the move. Perhaps the stressor and the resulting behavioural issues were not dealt with well, and she is kind of locked into her new behaviour.
I think some research would help you out - besides the books recommended already, I would recommend asking for advice on a cat forum like Petforums. Describe your situation in detail and you hopefully will get some good suggestions. There are also a lot of posts about weeing inappropriately on this forum, which you could have a browse through.
In the meantime you need to manage the situation so you aren't so stressed yourself. Can you keep the cat in a limited area of the house? Perhaps the kitchen or somewhere where there is nothing soft or tempting to wee on like carpet or sofas (and if she does wee it will be easy to clean up?) You can put a feliway plug in the room, and you could also try Zylkene, I don't know if your vet mentioned it? It is a natural supplement meant to reduce stress. If you do need to protect furniture you can buy water-proof picnic blankets - the cat may pee on them but it wont go through the backing. You could also use cheap shower curtains to protect furniture from wee.
You could also call a cat behaviourist if you have the funds, I assume their job is to come in and figure out what the source of the behavioural problem is fast, which you would find helpful!
Good luck.