I'm a Calvinist so I would agree about all those strong statements about people always being in the grip of grace.
However -- if someone forsakes their faith and/or lives clearly out of accord with the moral law, then the church is obliged to say, "All evidence says you are NOT a believer, for you would have repented given the opportunity." Then they move forward with discipline.
Your wife NoCode (as well as Olive's Husband) must realize that one have cannot Jesus as Savior if he is not also embraced as Lord.
Is he your Lord? Yes or No.
If Yes, then cease and desist from the affair, immediately.
You can't have 50% of Jesus. It's an all or nothing deal.