I am so sorry that your cat is being so stubborn.
I agree 100%, her food, water and litter should remain in the bedroom which she has taken refuge in. Some cats just need more time than others.
Since the new cat doesn't sound like a threat to her, I am hopeful that she will get used to him in time. the Feliway might help. And you might even wish to talk to your vet about medication to reduce her stress. Maybe there is even something natural that would help. Possibly some rescue remedy in her water?
Good luck! And thank you for not giving up, both cats need you.