You obviously love your DH and don't want your marriage to end. I don't think he does either, it's just that you two need to change how you interact together.
How about you go on your holiday, have the best time you can, don't mention anything more about all this. Let things pass uncriticised (obviously I mean small things, not bad stuff) and try and have fun.
When you get back and you are both calmer, why not try counselling together? That way, it would be less of a you-correcting-your-husband dynamic. If he hears advice coming from a professional, it might be better received.
He mentioned there are things that you do that bug him. Sounds like he keeps quiet about them for the most part. Maybe he feels you should do the same and feels it isn't fair that you raise issues when he keeps quiet. Trouble is, that doesn't get anything sorted. You both need to communicate more not less, so long as it is in the right way.
You say you have two young children, so your lives must be really busy and quite stressful at times, with not much time for the two of you as a couple.
It's likely that you just have a communication problem that could be fixed if you are both willing to work on it.
I wouldn't worry toomuch about what he's saying. It's probably just in the heat of the moment because he just doesn't know what else to do right now and is in despair of things ever getting better. He maybe was feeling okay about things, then received your email telling him he was wrong and felt like giving up. That's why I think you should work with professionals on these issues. Hand it over to them, as it were.
But definitely back off on crying and pushing him for answers right now. Try to centre yourself and try not to panic. Just enjoy yourselves on holiday and try and remember what you love about him.