If you check on your regional police authority's website you will no doubt see a page of propoganda information which states that they take domestic violence seriously.
If you are saying that he punched you in the face with such force that you were rendered unconscious and that the police subsequently arrested him, summarily cautioned him, and released him to return to your home that same evening, I am OUTRAGED.
Did you make a statement to the police? Regardless, the police should have referred you to a domestic violence counsellor and should have also explained that they are obliged to send a report of the incident to your local authority's childrens' services department - whether or not you are contacted by a social worker remains to be seen.
The answer to your question 'Do I let him stay in the house now' is an overwhelming NO and if he has, indeed, been given a police caution for this incident, you will have no difficulty in obtaining non-molestation and occupation Orders which will give you the legal right remain in the marital home and require him to stay away.
To this end I would suggest that you visit www.womensaid.org.uk and call the Helpline. As the 24/7 number can oversubscribed, I would suggest that you search 'womensaid' following by your county or nearest town and make contact with your local branch who will give you advice and support and put you in contact with a solicitor who will apply for the necessary Orders on your behalf.
You have described him he 'a good man who needs to manage his anger'. I would describe him as a man who sees no reason to manage his anger as he has become accustomed to taking it out on you.
It may be that if he attends an anger management or similar programme he will see the error of his ways and learn how to control/handle his anger. However, he should not live in the marital home again until such time as he as completed an intensive course and demonstrated over a further period of time that he has learned from it.
As others have stated, your little dd will have been traumatised by what she saw her father do to you and by her fears that you were dead. Is she at pre-school? If so, I would suggest that you make the school aware of what has happened as she may become withdrawn, or may act out, or enact the violence she has witnessed against other children. Ask her school or your GP to refer her, and any of your other dc who witnessed this incident, for therapy which may take the form of play therapy that will minimise the psychological damage that has been caused them - she/they will enjoy the sessions.
For the sake of your dc, if not yourself, please do not be tempted to let this violent man persuade you that he's learned his lesson, will never do it again, let's put this behind us, make a fresh start, etc etc, because, frankly my dear, he'll be telling you a load of asolute bollocks simply so that he is not unduly inconvenienced.
Please also be aware that you should not enter into joint counselling with an abuser.
I hope you will act on the advice above without delay because his next punch could kill or permanently incapacitate you - and I suspect that you know very well that there will be another punch or more in the not too distant future.
I further suggest that, should you choose not to act on the advice given to get him out of your home, you consult a solicitor with a view to making a Will and formally setting out your wishes as to who should have care of your dc in the event that you are severely injured or murdered by your husband.