Try not to dwell on it. You're safe & he backed off - if he'd meant to hurt you he would have tried to carry on. Like you said, he's not actually been abusive before, he was just being a drunken idiot, not that that's much of an excuse. Hopefully he'll remember & cringe tomorrow & not dare try any funny tricks for a while.
no funny tricks for a while- for a while is not good enough.
never. ever. again.
It is assault. sorry to put it in black and white but it is. so don't minimise it. he did something very wrong. if you don't make it clear that it is very wrong he will minimise this the same as he minimises his affair and everything else. he can't help it. he loves you. blah blah blah.
and next time (god forbid) he may escalate. I hope I am wrong. but just be on guard. don't let him terrorise you in your own home. make it clear next time it IS the police.
I know you know him and he has never been abusive before...but you never thought he would cheat, you never thought he would be such an idiot about it afterwards. he is full of surprises.
This is NOT a criticism of your awareness LNM. I just think that the way he has been behaving lately he may as well have been a stranger for how much he is different from the man you loved. God knows where this idiot sprang from but he is clearly not the husband and father you knew. IYSWIM.
and fwiw trying to turn the responsibility around on you, asking you to look what it is doing to the kids etc. is a form of emotional abuse as are the threats to move in with gf/not move in with gf, phoning you at all hours etc. as is cheating on you in the first place.
time to make a clear boundary- he does not come into the house if he does you will call the police.