Firstly, I'd say you can listen to opinions here, but you need to make your own decisions. Everyone has their own 'bottom line' in families and relationships, and you need to know and act on yours, not anyone else's. MN is great for advice, but it can also make you feel you should take one particular course of action; but in fact you need to work out what's best for you and your family. :)
Now my tuppence-worth...
There will no doubt be people along telling you that you should throw your husband out; but you've already said you want to "move forward as a family", so I'm assuming that is your starting point...
If everyone knows this was a colossal mistake, then I think that makes the situation a bit easier... How do you generally deal with mistakes in your family? I have tried to bring my children up to know that people are 'allowed' to make mistakes, but they need to learn from them, and they need to take the consequences of them, and if other people are involved, they may need to act to put them right... If everyone in your family believes this, then I agree with Hattifattner: you can sit down as a family and resolve this.
I also agree with H that your daughter needs to learn and is not just a victim in this situation. You don't say how old she is, but you give the other kids' ages, so I assume older than 14. She is not really a 'kid' any more, and it will be hugely helpful to her through the rest of her life if she learns that if you disrespect people, and 'push all their buttons' (which you say she did) some of them will lose their temper.
You might like to examine/challenge your own opinion that your husband has "marred the childhood of all three children". If he has been, to date, a loving and caring father, and this is out of character, and acknowledged by everyone as a big mistake, then I can see absolutely no reason why their childhoods should be 'marred'. They'll be shocked, yes. They'll remember it, yes. But they won't be damaged by witnessing their father lose his temper. However, they might be influenced and disturbed by you telling them they should be disturbed, so be very careful about that.
You say your husband is "a man of deep feelings and not good at articulating them" so I'd just like to point out that anger/rage are feelings too. If he doesn't usually express his feelings, and he has now, and he gets the message that this isn't 'allowed', then he's more likely to repress emotions in future. You might say it's a good idea to repress anger (certainly we all get very mixed messages about that) but it's hard to repress one emotion without repressing them all: if he's 'not allowed' to express anger, the chances are he'll be less good at expressing his love, too. :(
I'm not saying it's OK for your husband to rage and hit people. (You very specifically said this was out of character, and I'd be voicing very different opinions if you hadn't). It does seem possible that he needs some support with dealing with anger, especially since you have other kids who will no doubt 'push his buttons' over the years to come... The difficult thing about anger is that it needs to be expressed, but without hurting anyone... And the difficult thing about teenagers is that they can make you very, very angry - sometimes accidentally, but also sometimes deliberately. I have sometimes thought that the reason we struggle so much with teenagers in our society is that we are a bit rubbish, generally, at dealing with anger... 
Anyway, some kind of parenting course might help you both :)
Finally, I'd just like to say that I am someone who has never tolerated violence of any kind in any relationship - and I have always thought that if someone acted violently towards me, that would be the end of it. Then a few months ago, my own son 'lost his temper' - several times - and he is much bigger and stronger than me, and it was very frightening. If he had been anyone other than my son, I think I would have thrown him out. But when it came to it, I realised the 'equation' wasn't as simple as "no violence or you're out". Personally, I found my bottom line was "no violence or I'll have you arrested" - and I did - but I let him back home; and actually, I find other things - esp. breaches of trust and disrespect - are harder to forgive than a loss of temper.
I do understand how an incident like this can shock you so much, and challenge your 'core values' so fundamentally. It takes time to work out what you feel and what you should do.
These sorts of situations are extremely complicated, and only the people inside a relationship or family can know all the ins and outs/pros and cons, and can decide what needs to happen. It may well change how people feel about each other - that is one of the consequences of 'big mistakes' - and some of those changes may not be good. But long-term, some changes can be positive, even in miserable situations like this - for example if your daughter learns not to 'push buttons', and your husband learns to express his anger in a more controlled way, and you learn that you are a better diplomat and problem solver than you ever imagined! :) Good luck!