My brother was an alcoholic and, for the sake of their 6 year old DS, SIL divorced my brother. He came to live with me. At first, it was supervised access at my home - SIL, her sister and DN came for Sunday Lunch.
After 6 months, SIL decided that DB had proved he could stay alcohol-free before and during meeting with DN. He appeared to be clear about not drinking whilst in charge of DN and so she allowed him unsupervised access for 3 hours on a Saturday. However, DN was told that he must NOT go into a place that sold alcohol because it would tempt Daddy to drink. It did happen once, DB suggested a place for lunch and DN spotted the booze. He turned around and said, "No Daddy, we are not allowed to be in a place like this." DN told SIL as soon as he got home - because there had to be no secrets. Unsupervised access was cancelled immediately even though DB protested that he was just going to have a sandwich.
(DB was not an aggressive alcoholic - but he couldn't look after himself when he was 'in his cups' never mind look after a 6 year old in the middle of a busy city! I say this because DB wouldn't have been 'shouty' with DN - that wasn't how his alcoholism manifested. )
Supervised access occurred in her home after that, but I did have to phone SIL on a couple of occasions to warn her that I thought DB had had a drink in his bedroom and not to let him in.
LN adored his Daddy and loved seeing him - but DN's safety was paramount. DN knew about Daddy's drinking because he had lived with it so it felt okay to explain to explain to a 6 year old what must NOT happen when he was out with Daddy.
Sadly, our truthfulness helped DN to understand when his Daddy died suddenly with alcohol toxicity (DN was aged 7.5 years). When DN was brought to my house for the funeral I was trying to be a bit too bright and bubbly for his sake. DN asked if he could go up to Daddy's bedroom to find something he had left, so I went with him. On the way down the stairs he stopped and said, "You do know that my Daddy is dead don't you? Mummy said that he had been drinking took much and became poorly again."
DN is a happy, healthy, well-rounded 13 year old now. He has very fond memories of his Daddy.
I guess I am saying that you HAVE to be honest if you are going to allow unsupervised contact. They HAVE to be able to tell you if something you deem to be unsafe occurs. (And that is ONE SINGLE DRINK - because the alcoholic is sneaky! If the children spot one drink, how many more might have occurred in the bathroom/bedroom with a hidden bottle?)
I have found it hard writing this. I hope it helps you in some way to reach a decision that is right for your children.