To answer your question about the exposure, you need to use it for when it's the most beneficial for you, as Job wrote you can use it as a negotiating tool to get something or I will add as something to create a small wake up call. It depends of each situation.

You cannot expose without proof, so copy anything you can and create a timeline of it. Do you have letters from her to him? What's inside? Does she write about her current boyfriend? Do they meet? Did he promise her to live together? basically who is the one who is the pursuer is their relationship? Who has the most to lose if some facts come to light? Is she really into him or just being flattered to be pursued by someone? some women just like the attention? May be right now, it's in your best interest to just keep monitoring their interactions, you don't want to expose your sources too soon.
If he moves out, she will have to make a choice, staying with her current boyfriend or with your husband, decisions will have to be made, talking is something, doing is something else (fantasy versus reality). If she decides not to move with him, he will then be hit with reality. Even in the event she moves with him, do you think her lifestyle/personality will be easy with how your husband like to live his daily life.

His spewing is a way to provoke you so you can get into another fight/argument just to confirm/justify his decision to file for divorce. Don't fall for it! Detach! Ignore them but keep/archive them, just to show how irrational and aggressive he can be in case you need to prove how unstable he is. In return, be very careful about what you write to him. Stay always "very professional".

Don't stop him to be with his son, keep him updated about what you will be doing with him, now it's up to him to join you or not, by doing that you leave him the choice, but keep your activities (GAL) private. My husband reconnected with his kids well before he did with me. If he sees what a great/dignified mom you are/were, it's something he will be very thankful for, if one day he comes out of his twisted world. The high road is never something lost down the road.

Being detached doesn't mean being cold so just treat him as a "nice neighbor", polite but no more. When you make coffee, offer him a cup or whatever you know he might appreciate (small gestures only), and keep track how he reacts, he might say no one day (don't be offended, just move one), he might say yes the other (also don't try to engage in any R, just move on).

Give him space.

Stay away from any negative circles that for your best interest.

Remember it's impossible to make him change his mind with any conversations, his mind is totally irrational right now and he sees you as the enemy, because if he feels that way it has to be because of someone, so don't give him the "treat" to validate those thoughts. Let him figure things out without you in the middle the least possible.