She sounds like a good candidate for rehabbing and homing. I don't see why she can't go in and out. Other people here have done that. That would build her trust. It would be safer for her to be an indoor kitty, tho.
As for peeing on things, if you get her a large litter pan with some play sand or clean fill dirt (NOT potting soil) mixed so it looks familiar to her, and show her, she would probably get the hang of it. Or she might want to go outside and do her business. One of my neighbors has an I/O cat and he PREFERS to do his business outside.
Also - if you have resident cats ... you may want to keep her separate unless she is UTD with vax and flea & worm treatments. Is she one of the ones you had fixed? Does she get along with your cats and them with her?