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Not as rude as "harlot," "whore," etc. "Cheater" doesn't work, because really, he's the cheater, not her so much. She's not exactly ethical, but all the venom should hardly be reserved for the person who did NOT break marriage vows.
"lover," "paramour" gives the relationship more legitimacy than it deserves. Too Harlequin, star-crossed romancey than they deserve, particularly in light of his chronic hypocritical moralizing. Note to GOP: if you're going to be a manwhore/airport bathroom pervert/hooker hirer, you might want to save your sermonizing for the audience in your bathroom mirror.
As for an appropriate name to describe him, nothing printable comes to mind.