Not long ago I saw a copy of a tweet from Kaine (IIRC it was within the last couple of years, the tweet thing), saying that he and his wife had an open marriage so she could have other lovers, and it was fine with him. Paraphrasing.
I just searched and found a copy. Snopes says it isn’t real but snopes is full of crap. It should be easy for a technical person to determine if it is real or not.
The fact that Kaine disappeared immediately would indicate the open marriage thing is true.