I read your post, I won't deal with all of it,just the tail end of right now, who were you punishing when you dropped the kids off at her place early that morning?
Her?
The kids?
Both?
You assumed she was hung over and yet you still dropped off your young children to be in her care while she was hung over and you probably knew she would be angry and take it out on them but you still did it anyways?
You brought the kids there and I'm pretty sure you knew the reaction you were going to get and on top of that you got to leave, your kids had to deal with an angry hung over mother.
Does that make you a good dad? A good spouse?
All I see is one-up-man-ship, you do something to her, score 1 for you, she does something back, the score is now even, she does something to you, she's up by 1 now, you do something to her, you back at even score now.
Stop it.
The kids deserve better parents on both parts, I won't reward your behavior or hers based on the description you provided.
Excuses don't explain and explanations don't excuse.
Remember that, burn it into your brain and maybe you'll learn to stop evening the score.
Another thing you both need to learn but we'll focus on you right now because you're the one who is here and she isn't.
Resentment breeds entitlement.
It means in it's most basic form, you get angry at something she does, so you think you're entitled to something to even the score.
It's called maturity, you have kids now so you have to act mature. You don't have a clue about being a parent with young kids, well if you can go on this forum and post your story, I'm sure you can google what needs to be done with kids.
Focus on them. Stop pursuing your wife.
Don't call her, if she needs to, she can call you.
If she is just as immature as you are, I would consider this separation a blessing in disguise. Take care of those kids who didn't ask to be in this situation and be the best father you can be. If your wife wants to be with other guys since you had an affair, let her, you couldn't stop her if you wanted to.