It doesn't matter if the kids, parents, family, friends etc. all think the sun shines out of his arse. They aren't married to the man who shags other women. You are! Do they have any idea? If not, perhaps you should put them straight. Don't worry about bursting the family bubble. He's the one who should be worrying about that, not you.
if you have previously had 'concrete evidence' and say you have caught him again this week then his cheating is beyond dispute, so it doesn't matter how much he 'blames you, minimises and all the rest of it. You know what the truth is and the truth is that he has destroyed the marriage, not you. He's the one who's been screwing around for 10 years. Not you. So you need to keep that at the forefront of your mind at all times. Even when others are telling you how great he is, even when you are thinking about your (nearly grown up) kids and worrying about how devastated they will be, and especially when he is standing in front of you lying his cheating arse off - although hopefully you won't allow that to happen.
If you seriously want to get rid of him, you then need to stop engaging with him and letting him lie, twist and manipulate. If you don't engage with him, he can't do it. Don't give him the opportunity. Don't give him the chance to talk you out of it. He's out of the house now and you have a golden opportunity to start putting the wheels in motion to separate and also to make it absolutely clear to him you you don't want to 'talk' to him. The talking is over.
I'd also tell people, I really would. If you keep covering up for him in terms of keeping his philandering behaviour a secret, and keep letting him 'talk' to you, nothing is going to change. Same behaviour brings the same outcome.
But If you seriously mean business this time then start taking some action. Talk to people (coming here is a good start) get financial advice, legal advice, get paperwork together, plan your escape, get some RL support - you mention a friend, are their others you could get onside?
The good news is that if you are are 'happier when he is away on business', then that says a lot. It shows that emotionally you are in a stronger position than most with cheating husbands. You sound like you've reached the end of your tether, and I don't blame you. Over a decade of cheating with multiple women? I wonder if some of those people you mentioned who think he's so 'great' would still think so if they knew what a lying, cheating scumbag he actually is?
I'm not writing terribly well as it's late and I'm knackered, but I didn't want to ignore your post. Hope at least some of the above made sense.