Awesome that you went back to church, keep going, patience and prayer!
Also, first thing you have to understand is to stay off Alcohol for a while.
It will help you get your stuff in order and will prevent you from feeling the urge to do stupid mistakes while intoxicated and the day after, like calling her, texting her, sadness, anger, etc. So stay off of it is my suggestion.
When she asks you about doing things that involves the kids I don't see why you shouldn't after all they are your kids and you're trying to be a better person that is understanding.
Now if she had asked you to just go to the store to just get her a bottle of wine than that's a different story.