Make her want it. Women are harder to arouse, have a harder time reaching orgasm, and have a pretty major incentive to avoid sex given what pregnancy will do to their bodies. Regardless of whether you're using blackmail or drugs or whatever else, make her want sex. Indulge in fetishes she has but has never had the courage to explore. Get her mind focused on sex even in nonsexual situations. Use toys to build up explosive orgasms. Drive her to a point where the sex is so good, so ingrained into her life, she stops caring about all the reasons to say "no" and just enjoys herself.
In the specific example of your game, focus on the fetishes. Give her some repressed sexual fetish she never tried before (or give the player the chance to choose it at the start of the game) and then offer clients who are willing to pay more for the fetish acts than for standard sex. This will change the prostitution from something she has to do into an outlet for her own sexual desires. As she starts to enjoy the work more she starts shopping based around the needs of the job. It can start off simple with sexier clothes, grow towards sex toys and props for clients, and eventually she'll be buying furniture and artwork to create the proper mood for clients she brings home.