You're trying to let her "normalize" things too much. Tell her she has the two options (which are outlined above), but if she chooses "no if affair is still going on," that you will suggest a SCHEDULED visitation arrangement regarding the kids. And under NO circumstances will you allow her to put them in the middle of her own mess by doing things like ASKING THEM WHICH PARENT THEY WOULD LIKE TO LIVE WITH! That was just unconscionable.
