Hi Hope907 and welcome to SR.
Sorry for what you are going through. I suggest you search the forums here you will find much support in people who are going through or have gone through the same.
I highly recommend you start attending Al Anon the spouses of alcoholics are often codependents and enablers focusing much attention on the alcoholic in their home, and not so much on themselves.
Deciding what to do in this situation takes some time and refocus of energies off the Alcoholic, and focusing on what and how you want to live your own life. Alcoholism is progressive and it sounds like your husband has a physical dependency to alcohol based on his routine of drinking very early in the morning then throughout the day.
While you husband may not be "abusive" in the sense of verbal or physical action living with an alcoholic has many ramifications aside from physical and or verbal abuse. Alcoholics really aren't emotionally supportive or capable of participation in relationships or parenting. While you may feel the divorce was hurtful to your children, living with an alcoholic parent under the best of circumstances also has terrible effects on children that last a lifetime.