Hi OP, just read all your posts. Well fucking done you! You've done brilliantly and if I was your IRL friend I would buy you all the wine 
If it helps, you could lean into the rage when it comes, like today. Go and scream and swear somewhere, where no one will hear and you can be as loud as you like! It's good to feel that getting out of you!
So I've not been cheated on by DH but we have been together 20 years and last couple have been rocky AF. He lied to my face about drinking and then got caught out. The circumstances were truly shit - I had just had DC2 and was co-sleeping with the baby as he was teeny and underweight and we needed skin to skin. I told DH, lovingly, that he had to not drink because of the baby, or if he did drink he had to sleep in the spare room. He agreed. Then he was all slurry and messed up and I said "drunk?" and he said "no, just tired - you're being hormonal, and paranoid" etc etc. This went on for days, I felt like I was losing my mind. Then I found the multiple empty bottles of vodka... 
What I've felt over the past 2 years has really evolved. In a nutshell, I've stayed, and things are getting better.
The first thing was total despair, rage, betrayal. Trust is a red line for me and he broke it completely. How could he choose booze over the safety of our newborn baby? How could he gaslight me like that? Who is this cruel immoral callous stranger in my house?
Then I felt the weight of what a breakup would mean, for our kids (who are much littler than yours and far less emotionally intelligent!) and for us. I felt massive pressure to stay, massively trapped by that, and that I wasn't strong enough to split up. I hated myself and felt weak and guilty and ashamed.
Then I did some deep work with a counsellor about families and patterns and inherited pain responses. I have my stuff, definitely - my mum died young and my dad abandoned us kids soon after and I found becoming a parent re-triggered a lot of my trauma.
I think basically that the same thing happened for him - in his family his dad was an alcoholic, his mum is pretty emotionally withdrawn, they broke up when he was 9 and he suffered a lot of grief but being an only child he had no one to talk to and suppressed a lot. Becoming a dad re-triggered a lot of this but he was still really closed off and saw no way to cope except the booze.
Seeing so clearly how those patterns we had mirrors our parents' stories, I was hyper-aware that the chain goes on past us - we already have kids. I really had to think about how I could try to END some of the patterns with DH and I, instead of tying them up in a bow and handing them on to our little ones. That was a massive motivation for me, trying to end the patterns with us.
DH has done amazingly the past year especially - seen a trauma specialist, done EMDR, had counselling himself and been with me at couple's counselling talking it all through.
He's heard me say that I don't want words anymore, I want actions, and he's done stuff - brave stuff - to try to be that person.
I think that the cord between us, that I thought he had taken a machete to with the lies, wasn't broken - or if it ever was, then it has somehow mended. He's human, like I am. He's fucked up, like I do, like everyone does.
I still love him, I still fancy him, he loves our kids, he still loves me. We've built a life together that I'm proud of.
I think the more he deals with what happened, the more he's turning into a pretty great role model for our kids. It's part of being human to make massive mistakes, and what matters is what you do after the massive mistake. He's taking responsibility. Honestly, I'm proud of him.
I'm proud of myself too - for not putting all the shit into some 'evil unspeakable ex' basket and wrapping myself in a 'perfect blameless victim' cloak and running away. I've accepted that there are 2 of us making this marriage and part of the distance that developed between us, the carelessness, the not valuing each other, not noticing each other's pain - that was from me, as well as from him.
All of which isn't to say that I'm sure we'll be together for ever, BTW. I have no crystal ball. What I did feel, when the shit hit the fan, was that I COULD leave him/make him leave - I COULD live without him, I could be a single mum, it was a manageable thing for me. That was sort of unthinkable before, and it gives me some strength and confidence to know that.
Anyway, this is a ramble and you might feel it's totally irrelevant. I just wanted to share in case anything is useful to you. You're doing great and I wish you and your DC all the absolute best things. x