I'm so sorry. I was in your shoes, many years ago.
There is no rationalising with someone who depends on drink (or anything else) to get through the day. The drink talks louder than you.
Sometimes they are outright lying to you; sometimes they are kidding themselves. In my experience, Ex-DH developed an ability to lie really convincingly, to come up with excuses he needed to leave the house (to get a drink), or encouraged me to go out for the day (so he could just drink), to break away from the group on holiday (to sneak to a pub), to drink in the house without me knowing (drink hidden in some weird places).
Sometimes I knew I was being lied to; many many others I learned after. I know that I'll never know the full extent I was lied to.
In the end, the drink (actually far earlier than that), the drink was more important to him than our marriage, DCs, work, friendships, family relationships, being healthy).
The sober him was a loving husband, devoted father, caring son. But once addicted, the drink talked louder than everything else.
When I was in your shoes, I tried rationalising, asking why he lied about going to the pub, pleasing with him to talk to someone about it, showed him statistics, told him that, no, it isn't normal to not go a day without a drink. It isn't normal to hide alcohol around the house. It isn't normal to lie to your wife so you can conduct your affair with drink. Sometimes he'd agree with me (either to shut me up or because in the later years there were moments when he accepted it, but they soon passed because the drink spoke louder). It begged and pleader, shouted, encouraged him to book on recovery courses, AA.
Eventually I realised that there was nothing I could do. And I left. He was dragging me down with him. I was suffering mentally. I wasn't being as good a mum as I could be because of that. I'd realised he'd driven the DCs at least once while drunk. He'd become an unreliable father. He was still extremely loving but couldn't be relied on to remain conscious while the DCs were in his care.
That was many years ago and I haven't regretted it once. I wish I'd left sooner though.
Please look after you, and your children. When you live with an addict you can spend all your time and energy trying to manage them and their addiction, worrying what mood they'll be in, whether they're lying again, are they capable of looking after the children? While they spend all their time worrying about the next drink.
My DCs, despite adoring their dad, flourished once we lived separately. We'd all been living under a kind of stress. They had their real mum back.
I wish you well.