I nursed a parent through alcoholism as a teenager. I went to their funeral before I'd even left school. I thought in my naive undeveloped brain that I could save them because they loved me. They did genuinely love me but it just isn't that simple.
Love doesn't cure an alcoholic, you cannot help them if they don't want it, and if he's not even embarrassed enough to hide it from your parents (your second hand embarrassment did) then you cannot help him.
Think about this from your DCs perspective, as it's not your fault they will have to deal with this at some point in life but don't have another baby with him.
They'll think he doesn't love them enough then resent why he can waste money and his time on alcohol but not give them time or even money for essentials.
They'll invite friends round to play and the smell of stale alcohol is in the air, or he comes to pick up from school and the teachers and other parents can smell it? It's actually worse for an older child because they then have to carry that embarrassment too.
As a grown adult with children of my own, I can smell alcohol on someone immediately now. I can smell someone who drinks heavily, it's in their clothes, their sweat smells different, his side of the bed probably smells of it even when he has held his bladder.
You say he's a committed dad but is he? Ask him right now to give up drinking for life or lose his child, and I bet he doesn't react with horror and want to change. He'll get angry, deflect, say really mean and not true things about you to remove the heat off himself, minimize how much he drinks or the effect it really has, he might clean up a bit for a few weeks even but unless he goes to groups, and goes completely alcohol free and engages with the GP I wouldn't even entertain that he's serious.
I don't mean for this to sound harsh OP this isn't your choice or want, you want him to get well and for your family unit to be happy and well. Your not in charge of him or his decisions, or responsible for the hurt he'll cause.