My dad is an alcoholic too, and although he never physically hit any of us, he was emotionally abusive and manipulative (as I think all alcoholics are). And, my mother was the stereotypical "enabler", so I have some understanding of what you are going through.
I think that it is very difficult to ever get to a point in life where you "forgive and forget", but I think that it is possible to accept that, through no fault of your own, you unfortunately had a very difficult young life and that it has left some inevitable scars. If you can accept this (and is sounds like to a large extent you have already) then you can start to move forward, knowing that the experiences that you had as a child did shape who you are to some degree, but they do not have to (and should not) define how your adult life will progress. The hardest thing for me to come to terms with was the fact that I could never change my father's behaviour, that he was unhappy and that his primary relationship in life is not me or my sister or my mother, but with a substance and there is absolutely NOTHING that I can do about that.
I think that it is absolutely the right thing to do, to keep your father out of your life at this point, but I understand that there is an inevitable period of mourning for the relationship that you have always wanted with that person, and that you will probably never have. Counselling is a good idea and I think that you also have to allow the notion that you are suffering from a type of grief to be considered.
Your own children have something better than a grandad to love (and that is not to say that a good grandfather is not a blessing); they have something that you did not have - a loving, positive and stable family - and as you know that is the single most important and most beautiful thing that you can give them.
Nurture your own family, mourn for your lost relationship, and know that you are doing the right thing.