It's your marriage... I would go right to her mother and say
I am sorry but there is already too much lying going on... I will not keep secrets from my wife for you or I am just doing more damage to my marriage than OM has already done.
I am inviting you to work with me to REMOVE OM from this marriage and do what we can to repair it. And starting that by lying to her is something I won't do.
I love you and your daughter but this has got to stop. It's not fair to me and keeping secrets of any kind isn't fair to her.
I hope you will do what you can by not supporting her affair and refusing to ever accept OM into this family. Your daughter needs to know the OM is a dead end.
Dont' push for agreement, you just WARN her where you stand and go...
