You stop yourself going under (IME) by being angry and by channelling that into making yourself a new life. You feel exhausted because you are still giving him headspace. Don't - and certainly don't do any more "counselling" with him. That is not doing anyone, including your DC, any good, it's just giving him a platform to pose on and justify the unjustifiable (can you tell I've been there?)
Every time he comes into your head think "fuckwit" or whatever abusive epithet you attach to him and push the thought away. He doesn't deserve anything from you, not even your thoughts. Don't talk to him, don't work around him. Don't enter into discussions of who sent what document when. He does not exist.
Communicate only by email - preferably one kept just for that purpose so you don't have to see him in your usual email account (set up a rule to forward all his emails automatically to a new email). If he doesn't stick to a time for seeing the DC he loses it, definitely don't run around sorting alternatives. Your DC are old enough to deal with him direct if they want to see him, you don't need to be involved.
Focus on you and on friends and leading your life how you want to. Let him have his 3 week luxury holidays with OW, they won't escape who they are.
And FWIW I think it is perfectly fine to feel angry and bitter - why wouldn't you? The person who was supposed to be the closest person in your life dicked you over in the most painful way - are you trying for sainthood? No didn't think so. Get angry with him, he deserves it.
In time you'll care less and less and you'll love your single life more and more - that's a promise,