I'm only giving my opinion because you asked. I would not send her to a shelter period. I don't think she would want to live like that or they may euthanize her. I say let her live as you have her. She can stay in the basement if she is comfortable there which I'm sure she is. Do you remember Maxine the cat I wrote about? She is still living! Some cats just won't get along with other cats or people. That doesn't mean I would give up trying though. I learned a lot from the show My Cat From Hell and other useful tips on the internet. I do hate that she could get hurt outside but I think she would rather live her life like that then be caged unless it is a really big cage and in your home. It is good that she has socialized with you and that is a good sign. That's just how some cats are as you know. Did you try feeding them close to each other but not where they can get into a fight. Don't know if this helped at all but good luck!