I’d offer her $500 and a free moving truck. $500 (assuming you have it of course) seems generous I know, but throwing some cheese in front of her getting her to leave compliantly is very likely going to be quicker, easier and quite probably cheaper than any other solution.
Get the keys to the car, secure all your valuables.
Don’t have sex with her again. Seriously, just do not have sex with her again. “Whoops I forgot my birth control pills” = $100,000 – $200,000 worth of child support over the next 18 years.