You both sound as much to blame as the other.
You drank too much and fell asleep, he woke you up in time for the celebrations and you went back to sleep again.
Then you told him you were pissed off with him for not waking you at midnight (which is late anyway for NYE, you needed to be awake before midnight to see the new year in. And he did wake you in time for you to do that, but you went back to sleep).
It was six minutes after midnight when the kids woke you up. You hadn't really missed anything, but from what you've said here, it does sound like you started the argument and then recorded it.
His reaction does sound over the top and with everything else you've said about him I think he did the best thing by leaving when he did.
I also think you (and definitely your kids) would be happier if you ended this relationship and didn't start a new one until after you've had some time alone and perhaps some counselling.
You are not going to change his behaviour by recording him. If you feel that he's blaming you unfairly for something every time you argue, and you can't resolve that by speaking to him about it, then you're definitely not going to resolve it by recording him while it's going on.
If there is something abusive or toxic about his behaviour then all you are achieving by recording him to prove it is giving him an extra bit of ammunition to throw back at you.
And ultimately, nothing you do can change someone else's behaviour. All you can do is change your own. And I think that might be the best thing you can do for yourself and your kids, probably through counselling (which I think everyone should have, as the more self-aware we are about ourselves, about our own values, our own good and bad points, and so on, the better and healthier our own relationships become because we bring healthy attitudes into them, and the better we are at protecting ourselves from those people who probably should also be having some therapy but won't accept they need it).