First thing you need to do is get a signature so people can better understand your situation. We don't know how many kids you have, what ages they are, their living arrangements, yours etc...
If your H is being passive aggressive and cheating on you in my opinion you need to get YOU and your kids AWAY from him until he stops his destructive behaviour. This is pretty standard for anyone drinking, gambling, doing drugs...
You said lease so that tells me you don't own a home with him... So there's no legal ramification to you moving to a friend's place.
We don't know your employment situation, who works, who doens't, day care, income levels or anything either... so its again hard to help there.
But if your H wants you to live there while he overtly cheats on you and just blithely denies it then you and your kids need to get AWAY from him.
I am not saying your marriage is over, but moving takes planning and you need to start doing that.. I do NOT think you are going to end this quickly and safely while living there.
Your H wants you to remain there to keep exposure down. He doesn't want the bad press that comes with you moving out on him and taking the kids away... He KNOWS that's public and he KNOWS it makes him look bad.
If your H wants it quiet, then you make it as NOISY as POSSIBLE.
Why are you so obsessed with evidence?
You said you have a photo of his boss naked.. That's pretty condeming in my opinion... just get all the info you have to someplace SAFE... he will destroy it if he can.
