As others have stated, you do know who your wife is: a person with a high sex drive who needs variety. She told you this up front. When you married her, like any person who gets married, you take her for better or worse and you can't start thinking you can change her. It's like marrying someone who smokes 2 packs a day, but then laying down ground rules about quitting or cutting down after you get married. The time to ask for change is before marriage, and if you can't handle the reality, don't marry that person.
You have a wife who will likely want to sleep with other men on a regular basis for the next 20 years plus. Can you handle that? If so, tell her to come clean, and work out a reasonable arrangement where you can both feel safe. Talk about all the risks, insist on regular testing, what will you do if she gets pregnant and you don't know who's baby it is.
Also, find out if there are underlying issues driving her to be this sexual. I'm a highly sexual female, but I can't imagine needing to sleep with that many different people during the week while my guy was away. Maybe a boyfriend or girlfriend on the side, but it's the sheer numbers that makes me think that she needs too much ATTENTION and that is a sign of a self esteem issue. I say that as someone who has been there.
From this point forward, though, she has to tell you the absolute truth, whole truth, etc. Your life and that of your child is paramount and you need to know what she's doing, who is in your house, and what she could be exposed to depending on what sex acts she is doing. Is she having unprotected sex? Is she on the pill? Sorry to be a bitch, but are you sure it's your child?
If you cannot trust her, then there is no relationship.