Write it all down if it helps.
I am guessing the house is in both your names, so you pay half the mortgage.
Your children live there and you don't want to unsettle him, neither should he.
It would be easier for him, as the main earner, to find a house to rent. I don't know if you work but if you don't then you might struggle as a lot of private landlords don't like taking in HB claimants.
So logic and reason dictates that actually he should leave and get a place of his own, however without his mortgage contribution you might struggle so make sure you get CAB advice - you can't get HB payments for mortgages.
I think you would fare better with some real life support around you, so do open up to people. Tell them what is happening so that they can offer you support, don't wait until he tells them his biased version of events - get in there first. Your story will be the one they remember then, not his.
When you do tell him, if you think he is going to be unreasonable then have a friend on standby who can come round to be with you.
Yes he will try to blame you if he's a coward. Remember though that you haven't forced him to join married dating sites, you haven't forced him into treating you like a sexual object, you haven't forced him into being a liar. He is already these things.
Always be ready to turn it around and ask what he would do if you behaved in this manner? You already have an inkling of exactly what he would do, so remember that and use it to your advantage. Don't feel guilty, after all he didn't feel guilty when he falsely accused you did he? He didn't feel guilty when he told your friends and family and he still doesn't feel guilty about using it to silence you during every argument.
You've given him plenty of chances, he has betrayed you, he should do the decent thing now and make plans to move out so that you have the freedom you so deserve.