To invite or not to invite?

So, I have a predicament. My MoH is presently married. She has had an affair with one of our groomsmen (the affair has been made public, so it's not a secret - and please, I don't need a lecture about whom I've selected as my MoH). Anyways, she has said that she and her husband are going to get a divorce, but she's still living with him and they're still acting like they're married (going out to dinner together, etc.). My question is, do I need to invite her husband to the wedding? I'm worried that he might cause a scene at the wedding due to the affair, but hoping that if he is invited and does come that he'll try not to ruin our day with a fist fight with the groomsman.