Your goal is reconciliation OR divorce. Unless you want to live in an open marriage.
Again Starsky is right. No pronouncements. First talk to a lawyer YOURSELF. Find out your rights, protect yourself.
Also condsider what YOU want IF you got a divorce. Ask about things like child support, custody, etc to the lawyer.
Then take steps to protect yourself, like document how much time you spend with the kids, etc..
Then figure out how you are going to try to save your marriage.
You can try and work on yourself, get a life, etc, be patient and try to "nice" your spouse into picking you over the OM. Don't ask about the OM, etc. Be happy, detach, live in limbo for a while. Good luck with that.
Or you can try the last resort technique and see if it works.
If it doesn't you tey the AFTER the last resort technique (going dark) for a short while.
And if that doesn't work, give her an ultimatum. If she doesn't dump the other guy, apologize profoundly, write a no contact letter to the OM and go into counseling with you, it's time to walk.
You walk by 1. Either Filing for Divorce OR 2. Getting a Mediator or 3. Getting two lawyers who practice collaborative divorce.
Sometimes filing for divorce is the only message people really listen to and THAT might turn her around.
And...PLEASE, PLEASE read today's post on Chumplady.com It's painful, but it's where you may end up being soon.