Oh op I feel for you. But in your shoes I would certainly be separating, as per your plan.
He has shown a disgusting lack of concern for you. He has cheated. Paid prostitutes online and in person. Lied repeatedly over several years. And then when caught, he first of all minimises (he didn't tell you about visiting prostitutes in his first 'full confession' did he?) - and you can assume that he is still minimising.
He's lied for 3 years. He lied when caught out. Why on earth can he expect you to believe that he's now suddenly telling the whole truth?
So there is likely more to this than you now know. Very possibly there will be stuff that you will never find out. There is a very good chance - almost 100% certain - that he isn't telling you the whole truth, and he will protect that for as long as possible, ideally foreever.
And even if you do have the full truth now, it is still devastatingly grim. The lies, the cheating, the grim online and face to face with prostitutes sex. He has shown he has happy to lie to you and cheat on you.
Then you find out and he turns it around on you - it was because your sex life wasn't good enough. Well that is clearly a lie. But even if he was enjoying sex less should he a) have talked to his loving wife who has just had his child or b) find some online hookups and get his kicks elsehwere, while his wife struggles with looking after a newborn and her own birth injuries?
Aside from 'forgiving' (if that is even possible) how could you ever respect, trust or fancy him again?
Expect him to spend the next few weeks on best behaviour. He will see the few weeks grace as his chance to convince you that you've over reacted and he is the best husband and he loves you and is devoted and will spend the rest of his life making it up to you.
But if he was those things, he wouldn't have spent the last few years lying to you and cheating.
If you forgive him and agree to try again, I expect he will see that (in time if not immediately) as a sign he got away with it, so could do again. You would be telling him you're OK with that behaviour. And how could you ever trust him again?
He will do all he can now to minimise it, try to draw you in to somehow being at fault and part of the cause of it, to show you you'll be much worse off without him. He has a lot to lose - as pp said, his comfy home, respectable family, supportive loving wife, living with his children, the respect of his family and friends when they find out what he's done. He will be desperate to avoid that.
He has been his nr 1 priority while he's been getting kicks with other women for all this time, and that will likely continue now.
I'm really sorry as I know some of this sounds really harsh, and it must be SO hard when you've been happy all this time. And so easy for us on mn to say.
But I have been in a position where I had to make a tough choice, that would affect children. I did it and I never regretted it.