I wouldn't pay for her to move out. Maybe gift her the money for first months rent but really, if she doesn't work or have an income who would rent to her? If you pay for her rental you'll be stuck as landlord to a bad tenant.
Doesn't she have family she could move in with? Can't you call her parents, say she's cheating on you and needs to move back home, and let them deal with her?
I know I sound harsh here. But no way should you ever consider having children with this woman. Raising children together means having to support each other emotionally through some really tough times, and she's demonstrated she can be very unreliable.
Also - and I hate to say it, but it's generally true - someone who cheats during the first year of marriage usually was either having an affair prior to the marriage or at least contemplating it. Yeah, my exH cried at our wedding too - I thought they were tears of happiness, turns out an old girlfriend seduced him the night before our wedding.
