I can't advise you on whether or not to kick your son out, but I do think there may be another way you could handle the situation @Goodnan
First though...you said you've always had a good relationship with your son, yet it does seem you are jumping to the worst possible conclusions as to his behavior. I will play devil's advocate here and ask if it's at all possible that he's having outings with a female FRIEND that he doesn't want to talk about because of the potential accusations he fears would follow? Yes, it is improbable but not impossible and I speak from experience; when my DH and I were going through a rough patch 2/3 years into our marriage and he moved back home for a month or two, I found out he was seeing one of his female friends that I had only met once and was devastated. I hit the roof and was ready to tell him to get the hell out of my life when I found out she had called him to visit US with her new boyfriend and when she found out he had moved back home she met with him to hear his side of things, then gave him what for telling him he was a moron to leave and that he'd better work things out with me because he would not find a better partner. That was almost 3 years ago, she is now MY dearest and closest female friend and I'm going to be her maid of honor in her upcoming wedding. I understand my situation isn't the norm, but it is possible, so maybe try and have a little faith that he's still the good man that you raised.
Second thing I'm thinking is this, when a marriage is breaking down or having troubles it is tough on everyone. Again, you were very close with your son but I can see how IF he were to be acting a fool with another woman he wouldn't be honest about the situation to you. He knows you support you DIL and rightly so, but it seems that you've come at him in an accusatory and judgemental position (again, rightly so if he's fooling around with an OW). But! I think if you were to go to your son with an attitude of "I know you're having a tough time son, and I'm sorry if I've been harsh but you know I love DIL and DGD, it's been a shock for me as well as I've always wanted the best for your marriage. I love you dearly and we've always been close, I want you to know you can talk to me about what's going on, no matter what the case is."
You may have to bite your tongue a bit, and it IS manipulative, but if you REALLY want to find out what's going on, coming at him with "If you're cheating I will smother you with a pillow in your sleep for being a selfish prick!" is unlikely to be met with "Well now that you mention how you're going to asphyxiate me with my pillow...I'm shagging my new secretary mom."
So what I'm trying to say in my very long winded way is that one, maybe things aren't as bad as you're speculating and two, you might try easing off the accusations and judgement and try being the supportive mom you've always been to him in the past if you want to get to the bottom of things. For what it's worth, I'm sorry
that your family is going through this tough time.