There must be more to this story. Perhaps you're unable to pay the fee to have your vet treat your cat.
When we had a cat, the vet treated her for fleas in the office. I think his tech dipped her. He told us to bomb the house and air it out, before taking her home. I think our cat stayed overnight but I'm not sure. This was years ago. There are safer products now.
He treated her with a med like Frontline (I don't remember the brand) and told us to treat her every month. I know there are different brands with different chemicles. If one doesn't work I would've tried a different one.
The vet trimmed her nails at the same time. Cost just a few dollars. I'm not one to spend much money on pets. I thought the cost of having the vet to do this reasonable.
I don't understand your vet refusing to sedate her if it was needed to treat her. I might understand him to be unwilling to give you sedating medication so you could dip her.
Before taking my cat to the vet, I trimmed her nails by wrapping her in a heavy towel and having someone else hold her. If she hadn't been able to travel, I would've wrapped her in a towel, with help if necessary, and put her in a kennel. All my cats cried and screamed on the way to the vet. That didn't stop me from taking her. It's my responsibility to keep her safe. A parent takes a child to the doctor for immunizations even when they cry and scream. I decided to have someone else trim her nails because it was easier for me. Again my responsibility to care for her.
From your description of your car's behaviour, I suggest that she/he has serious emotional issues. You could find a vet that deals with emotional issues. Not all vets do. If he can't help the cat, I see no alternative to euthanasia.
Sounds like your cat has been forced to stay in a room and not been allowed to leave. I understand needing to do that. Sounds like no one has been able to befriend her or gain her trust. I accept that won't happen now. I suggest you've done all you can do. None of this is your cat's fault. Neither is it your fault. Euthanizing her is not punishing her. It's freeing her from pain and suffering. It's necessary for your sanity. I would not sacrifice my well being for a pet nor anyone else except possibly for my children. Then, I'd get help.
I suggest that by continuing so long to try with her, she is past being able to change. I urge you to have the vet euthanize her. I suspect he's suggested doing that. Perhaps you haven't been willing to do so because on some level you feel guilty and/or you expect yourself to solve a problem that can't be solved. It's past time to let go. Taking care of yourself should be your first priority.