You may well think or like to think he is a loving father for your kids sake (children will love any parent no matter how selfish they actually are) but the sad truth here is that he loves alcohol more than you, his children, well everything actually.
He is neither a loving father to them nor any sort of a husband to you. He may be holding down a job currently but for how long?. He has brought shame and despair upon your family. Your children are likely confused, embarrassed and upset by his behaviour as undoutedly you were when you were growing up with an alcoholic father. They can't bring their friends home on the weekend can the because they think what state will Dad be in?. They see that their friends dads behave differently, their friends dads are not drunkards.
Put yourself in your childrens position now; your mother perhaps stayed with her drunkard husband (perhaps you wanted her to leave him many times as a child) and look what it did to you. You ended up marrying a drunkard yourself. Do you really want this for your children; this is no healthy relationship model to be showing them is it?.
Seek proper legal advice to get him out of your day to day lives. Many solicitors will do a free 30 minute consult. That may all seem a step too far for you but do you really want to spend the next year in the same state as you are now?.
Staying sober for just one day now isn't going to cut it. Taking the kids out for the day is just putting a sticking plaster on an open festering sore; you cannot fully protect them here from the realities of his alcoholism.
Not really surprised either to see that he has relapsed or that you have told no-one he has relapsed. Its the big bloody elephant in the room and fear, shame and embarrassment keep you within it. Start talking to people about him and do not keep it secret any more, alcoholism thrives on secrecy.
His primary relationship is with drink first and foremost. Everything and everyone else becomes a dim and distant second even if they do figure on his list of priorities.
You will all be happier without him in your day to day lives.