"Honey, there is something I need to talk to you about when we get some free time."
Then let him set a time. He will probably want you to tell him right now...
"I want you to come home"
WAIT for his response.. LISTEN... LISTEN.. Listen to what he says and listen for the emotion behind the words.....
If he says no or balks.. DO NOT ARGUE.. Just say ok. Softly and matter of factly. You can't talk about the terms until you see what he says. If he says no, then there is nothing more to say.
If he says yes, then you have some decisions to make on how you are going to handle the affair issue. I believe you have to ask him to come home, but also be resolved that if he says yes that you say to him that the affair must be over.. AND if he says it is and you find out later that it isn't, that there will be NO other efforts by you to make this work....
Short sweet to the point..
The problem many of you women have is to TALK TOO MUCH. Most men do not like you to tell your point by going into every minute feeling, detail and word in your mind. Simple is better when trying to communicate with men. Long and drawn out is not a good idea.