The safety of the kids is paramount. I think it's a big deal if the lawyer is pushing for it. Usually, one of the parents wants it and the lawyer will indicate it likely won't happen because he or she knows what will push the judges in that direction. Your lawyer must have a good inkling that you will get it.
Do as your attorney advises and know in your heart that it's for the good of the children. Drinking around them and driving after drinking are very dangerous choices. You may be a little desensitized to his drinking if you've had to live with it for a while. That's not a judgment or reflection of you - it's just reality when you are more used to a habit. When an outsider, like a lawyer or judge, looks at it, sometimes a very different perspective is offered.
These are his choices. Dont feel bad or guilty about yours.
Hopefully, if he is ordered to have supervised visits, he will take it seriously and get some help for his problems.