Welcome back mns. I"ve got a very busy life too, not a single day of the week when my work, kids or myself don't have something planned somewhere it seems.
You are right that alcohol isn't helping. In fact, it's making it worse. And I think it's very important to view the drinking as separate and distinct problem. I used all of the things you listed as excuses to keep drinking. Of course I deserved a beer after running the kids here and there, right? Or after a particularly stressful day to "wind down" right?
The problem is, we drink because we are alcoholics. Doesn't matter if we are busy or not - we drink. And it's also very hard to be able to re-organize your life and prioritize things to make them less "busy" unless you have a clear head.
I hope you can find the strength to put down the bottle...that's the first step.