Since you’re still living together in the same home and not yet separated, you should hire a private investigator to ensure you have the proper evidence of the affair during the marriage (you must be able to prove an act of illicit sexual behavior), especially if alimony may be an issue in your separation.
A lawyer can help you to get her to move out by sending a letter to her and setting a deadline for her to move out, which will then jumpstart the negotiations of the details of the separation (dividing property, alimony, etc.).
If she refuses all of your attempts to get her to move out, and you do not want to move out of the marital residence, then, with your evidence of the affair/illicit sexual behavior, you could file a lawsuit against her for divorce from bed and board which could force her to leave the marital residence if granted.
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