I doubt they'd find out, since it's not like you get branded by a big scarlet P when you become a prostitute. If they did, I'd tell them that it was a job I did when I was younger and that I didn't have a problem with it, but because prostitution has such a social stigma, they should keep their knowledge to themeselves.
If my daughter/son became an escort, had attitudes toward sex to let them do it healthily, were taking care of themselves physically, and seemed happy, I wouldn't mind. If they seemed unhappy or wanted to quit, I'd encourage them and offer to support them financially while they got a normal job.
If my son/daughter started seeing prostitutes, presumably he'd have to be financially successful to be able to blow that much money on a luxury. If he was spending the rent money on pussy, I'd kick his ass. I'd try to make sure he wasn't seeing prostitutes because he was unable to form normal relationships. If he was just doing it for variety and not in a monogamous relationship, I don't see why I'd care.
In general, I don't want to hear a lot about my offspring's sex lives. Euw.