I'm so sorry you have to go through this.I know this is such a tough decision.She probably wouldn't do good here with my MANY cats.She doesn't like other cats?(is that the problem?)That is so hard trying to find a home for a cat that doesn't like other cats.Most people who are kindhearted take more than 1 cat and the other ones that don't care about cats have NO pets.That's why it's hard to find a home with no pets to take her.
Whatever you do is what you have to do.I would not like wondering if she got hurt outside either.(Or properly taken care of...and having her so unhappy).Not knowing is way to hard for me...so I totally understand what your going through.