You must understand that giving her an ultimatum will not save the M. If you are telling her to leave b/c of your personal boundaries that have been violated and b/c you refuse to live in an open M, then fine. But not for one second think it will scare or pressure her into giving up OM and stay in the M. Ultimatums are not the tools to use to save the M.
I will give you my personal feelings about it. I believe the WAW has to experience or see a loss due to her behavior. I believe if shenthins the H has "dumped" her b/c ofnher adultry, he would stand a better chance in R the M. MWD will not give you that advice. However, she does say that if the S refuses to end the A, to get a lawyer and file for D. (a lot of people seem to miss that sentence in her book.)
Get yourself together, get a lawyer's legal advice, confront her with your knowledge of the A (don't ask her questions, just tell her you know about OM), and tell her she has xx amount of time to find her another place to live (providing she doesn't own the house where you are living), and tell her you will not live in a M that has a third party. You make sure you are prepared emotionally and mentally for this confrontation. Have no expectations. Lay it out and leave it with her. Do not have an "in-house" separation! It will not have the same results. You must tell her she has to leave the home, b/c of the A. If you can't handle knowing what she's doing, then staying under the same roof in some type of in-house S will be much worse than things are now. To her, it would be the same as you knowing about the A and tolerating it.
You better be sure you can stick to it. Along with confrontation, your self-respect will probably rise a bit and you may feel a since of relief getting the truth out in the open. It is a way of picking up the reigns and being in more control. In many cases, if the WAW believes the H is dumping her b/c of the adultery, it will jolt her out of the fog and she will make an about face. But she won't do it right that moment. Certain things have to transpire first.
There are several things to consider. Is the OM married with children? If so, he may not be receptive to her news of wanting to get M and being scared she's pregnant. He may turn tail and run. She may use the pregnancy scare to pressure him. He may wonder if it's his baby. Your ultimatum could result in her running into his arms (but she's already there emotionally), but depending upon OM....they may or may not make it permant. That is why you must do it based on your boundaries, and not as a technique to break up the A.
Don't use an ultimatum as an emotional reaction and b/c you don't know anything else to,do to stop the A. You have only one good shot at it, so make it count. Don't use threats. Don't scream or cry when you tell her. Be confident and speak with assurance. Talk in a low voice, but very firmly.
Have everything set in place. Have it planned. Do not do this when you are reacting and upset. That is very important.
Make sure this is the route you want,to take. Once you do it, the worse thing would be to back down.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!