The marital home and particularly the marital bed is for the married couple. If she is in an affair or even in contact with someone with whom she had been having an affair, then she is not interested in being in the marriage. You cannot have a "marriage" of three people.
How do you approach that issue when she "wants to come back?" Well, you can't control her, you can only control YOU. So, you set boundaries to protect YOU (and your children if they are minors). Have you set a boundary with her that you won't share your W or live in an "open marriage"? If not, why not? If so, what would the consequences be if she violated that boundary? Other boundaries can be "I will not accept verbal abuse" (If that has been an issue) or "I will not lie to my children to protect your affair" or the like. Boundaries really need to be tailored to protect your own particular/personal value system. I was not awesome at defining and enforcing boundaries, though i think I ended up doing an adequate job in the end. There are alot of threads on these boards about boundaries, some stickied, i think, and you can google the concept as well. It is not unique to DB-ing.
H53/W51, R-ing 4/'18
"Do not arouse or awaken love until it so desires"-Sg.of Sg 2:7
"So oftentimes it happens,that we live our lives in chains, & we never even know we have the key"-Eagles III 1:3