As long as the EAs are still occuring, you are facing an uphill battle. SHe doesn't want to share passwords/etc with you because she is cheating. It's the simple.
Do not leave your home. If she wants out, she can leave.
Very clearly state to her that if she is involved with other people, it's not going to work between you to. No if, ands, or buts about it, If she wants out, again, she can leave.