You would ignore if you’re not going to do anything about it because it would make you look weak.

You would approach her and let her know that you won’t live in an open marriage and if she continues there will be consequences. If she continues you must implement the consequences. They must be strong. Separation/Divorce as an example.

If you want proof you can get proof. Phone records or a private investigator.

Better how? Because she’s nice to you? You took the pressure off so she’s nicer to you. Is there something else we don’t know about?