How can you tell if your wife is into swinging and prostitution?

Swinging and prostitution is 2 different things. Swinging is sex with consenting adults who usually have met before and is there for their own sexual enjoyment. Prostitution is having sex for money and for the paying part's sexual gratification. I doubt she is into prostitution. And the only way is to ask.

If you have problems in your marrige you can not talk about I suggest therapy. It very easily turns into scraming matches or ignoring so a therapist can help.