I know sure as heck that you don't chase or pursue or fight for a spouse that is actively cheating on you.
What does that communicate to them? To yourself?
That they're worth it?
Really?!
What about you?
All you're doing is communicating that you have apparently less value than they have because you are willing to tolerate a spouse that would cheat on you with another person, and boy oh boy, that brings them back fast every single time (note the subtle tone of sarcasm I've included at the very end).
Let her go, she wants out, show her the door, no worries.
You're not a prick or an a$$hole, on the contrary, you are happy and awesome.
Do you really want someone that doesn't want you? Is your self-esteem that low?
Sure continue with the outing? What do you hope to gain with it? You want to expose the affair, to remove it's secrecy and mystery, sure go ahead.
Don't do it to gain favor from your in-laws or kids or anyone else, that rarely works (if ever).
You tell her she can have the OM and you hope she's happy. And you do it with a grin on your face.
Ask her when she plans to move out because it won't work for her live at home with you anymore. Yes, she moves out, preferably within the next few weeks - maybe she can stay with the OM until she finds an apartment to rent. She chose to have an affair, she now has to deal with the reality of that situation, moving out, getting a place of her own. If you had the affair instead of her, you would have moved out. Be firm about this, you won't waver on this. If she has an affair and doesn't move out, tell her you will pack her things, put them in boxes, leave them in the driveway/garage and change the locks afterwards, if she calls your bluff, do these things and show her you're not bluffing. She will now be dealing with the responsibility of her finances, sharing responsibility of the kids, etc. She can file for divorce at anytime and you'll both sit down and tell the kids that you guys are separating.
Maybe when the dust settles from all of this "hoopla", you guys might even become friends.
Start working out, start shopping for new clothes/shoes, fresh look, fresh style and then start dating.
Then when the lustre of that affair wears off and it's no longer as exciting as she thought it was coupled with the fact that you will start dating other women soon, then we'll see if she doesn't come back asking to work on the marriage.
And you will be the one saying "hmmmm, I don't know, I'll think about it."
That is of course, if you really want to ;-)
This is just advice, given freely, in the end you have to make the choices & decisions that lead your life in the direction you want it to go.
My opinion is let go of the people that don't value you or the relationship they have with you. A spouse who chooses to have an affair and cheat on their spouse doesn't deserve your attention or the action of you chasing her, begging & pleading for her to come back.