1) If the guy wants you to take him out, then take him out. He's your long-lost visiting cousin. That bit's just ordinary courtesy. You are allowed to make it clear that he should have talked to you first about wanting to go out rather than just announcing it to your parents.
2) Your courteous duty having been done you do not have to do what he says/go where he wants to go/like him/conceal things for him or hang around like a gooseberry with he flirts up some woman. That's just your weird American moral culture kicking in, and you're entitled to it. If he moans about that, then that's him being discourteous.
3) If he gets antsy about that, either bring him back home or dump him wherever he is and come back home yourself and then (and only then) you have a sane reason for telling your parents about your concerns.
4) Do not try to contact the wife yourself. It doesn't go well. Not ever (well, hardly ever - I've only ever seen it work when it is a long-term close friend bearing the bad news). Gets you sucked in and taking sides in somebody else's relationship. Seen it happen many times and it is bad news. Chances are she knows what is going on, or at least knows what he is like - good odds this sort of thing is how he met her in the first place. Unless you know the score, don't stick your nose in.
5) But on the other hand, if you find out that he definitely is up to something, you do not have to condone it, support it or help him. Not your job, and goes way beyond the usual courtesy to visitors. Just stonewall him. He won't be back.