Your kids probably know the truth anyway, but if you don't confirm it for them, they may think some of this is their fault. THey need to knwo the truth, from you. You can tell your H that you are going to tell the kids the truth as well. I hid the truth from my two older kids for a long time and now they are 24 and 21 and I wish I would have told them the truth a long time ago. My two younger ones are 8 and 11 and they know all about alcoholism and are much healthier mentally for knowing the truth. They also know that dad's behavior (not being involved, cranky, sleeping, etc) are part of his illness. Your kids also need to know that it is okay for them to not get in a car with him if they think he has been drinking. So, yes, the truth is best. If you are uncomfortable, find a counselor who specializes in addiction and have the counselor help you tell the kids.
So glad you are coming here. This place helped save my sanity.