I lean towards High Treason's response but with some caveats. I think if he has sex with other women in the presence of your children, that would cross the line. But the mere fact that he meets random women, strangers, and rotates through them rather than has a steady partner should not have any effect on his legal right to visitation. He is within his right to decide if he wants to have sex with strangers or wants a steady girlfriend. I do not think that you can impose your ideas of what is and is not "high risk" on him via withholding visitation. I am not sure what you meant by "high risk lifestyle", actually? If you meant a high risk of STI's (you mentioned that he was having unprotected sex), then it is a risk for HIM, not the children. If you meant the general risk of having perfect strangers at home, then, perhaps, you can make this argument in court. If you meant the risk of drug use - I can see how random girls off online sex sites can also be drugs users with a higher likelihood (vis-a-vis non-users of online sex sites) - then you would definitely have an ability to make that argument in court - courts frown on drug use BIG TIME.

On a more practical note, Yoda is right - both the law and the judicial practice varies by state, so the best person to talk to you is a family law attorney licensed to practice law in your state. Anonymous internet users just don't have enough expertise to answer your query with confidence - we can only conjecture.