There are huge similarities in the way that I reacted after discovering my husband's affair. As someone said, I look back now with amazement at my responses but I've learned that shock is the most peculiar state of mind. My gut instinct was that this was survivable, but the adrenaline surge took me by surprise and was actually not unpleasant. All of my senses felt on high alert and during the hysterical bonding phase, it even occurred to me that this was what an affair must feel like.
But like an affair, this phase is not 'real'.
The really difficult stuff comes afterwards when the shock and adrenaline have worn off, so I'm hoping you'll see this as a kindness to pre-warn you about some things.
I'd also say that unless you've felt this way yourself, or have been through it, it's just impossible to say how you'd react. My own reaction shocked me too.
We learned so much from our individual counselling and from reading more or less everything there was to read at the time (was years ago, incidentally.) So I'll share with you that it's really common for the person who's the 'under-responsible' part of the couple to have an affair.
From what you're saying, your circumstances were different to mine, but there are some similarities in that my husband had let me take on too much responsibility for our joint lives and we'd got into a pattern of me being the one who seemed to have the greatest burden for keeping the show on the road, despite having a busy and demanding career.
You're right to look at your own behaviour but I promise you, this is too soon and I'd also judge that you're coming to the wrong conclusions about it. If you're partnered with someone who is either unable or unwilling to be an equal partner, unless you want your children to lose out or your own life to become chaotic and disorganised, you have no choice other than to fill the breach. It's hard not to feel resentful of that, but the answer is not to stop doing things or to somehow stop feeling resentful.
The answer should have been for him to take responsibility for his own health and his efforts to be an equal partner.
Instead of doing that, it's my hunch that rather than face up to those responsibilities, he secretly punished you for your competence and your justifiable resentment, by having an affair with someone who had no requirement for him to be grown up and responsible. All he was required to do was to be adoring and sexual and the same went for her.
As long as this thread is useful to you, it can be a very good thing to write down your feelings. I guarantee one day you'll look back and won't recognise yourself though. So don't make any irrevocable decisions and definitely don't decide that this marriage will work and you will forgive. It's a long haul and you can't know that yet.