Wow. I could have written your story. I will take a stab and guess that the hard booze has been happening much longer than you think, or at least it was with my X. He hid it in small bottles in the garage and all over the house. No matter. He's an addict. Just going to meetings is not going to make him well. If being arrested with a child in the car did not do it, what will?
I wish I had moved and and kept the focus on me and my children instead of my X. He too made me feel crazy because he would lie and then apologize as if that makes it all ok, and complete the cycle over and over. He too is a binger drinker. Eventualy it became dangerous and my children ended up being exposed to things they should not have. More importantly, I started to change into this angry, anxious person and could not even recognize myself. That has damaged my children as much as their father's behavior.
Please continue therapy and go to meetings, Alanon or Celebrate Recovery. I know our CR has free child care. This was a huge help to me. I knew I had to become strong enough that no matter what happened in my future I could handle it as my children need a stable, calm parent.
Sending you a big hug. Keep sharing, you are no alone.
Lastly....under no circumstance should your children be left alone with him, ever. He clearly cannot be trusted.