I have read on this sight that A's don't do things while drunk that they wouldn't normally do. Your A wasn't even drunk when she cheated. Seriously, how long was she in rehab? She couldn't refrain from doing that for that amount of time? She was supposed to be there to work on her issues. She was supposed to be there to focus on her recovery. If she had been doing the work she was supposed to be there for, this wouldn't have happened. If you are ok having a relationship with someone that cheated and will likely cheat again when presented with the opportunity, isn't serious about her recovery then I agree with you letting her stay and talk figure it out. I think she is using you. She could stay at her parents, but she is saying she can't.
I think you deserve better. I think any woman would be thrilled to have a healthy loving relationship with a good man. Why would you settle for someone that disrespects you and then doesn't show remorse for it?