It would seem your brother has major issues that HE needs to deal with. I'm guessing his wife's issues are overwhelming. Your description of her seems to me it's much more than simple laziness, but a deep and profound state of depression. I think a marriage or family counselor would be a good start, and then maybe it could lead to solutions for him besides cheating.

Unfortunately there's not anything you can do about it except be there for him if he wants someone to talk to.

My brother's wife died last year and it kills me that I can't take his pain away. I just make sure to answer all of his phone calls and texts, even if they come at 3:00 am.