I will preface my comment with the fact that I am not married and don't have any kids, so take my advice for what it's worth.
I think it's important that you don't push the "I want to come home" stuff on your wife when you meet tomorrow. Like others have said, she is most likely having doubts about how sincere your actions are based on previous events, so your pushing to come home before she's ready will most likely be offputting and just drive her further away.
If it were me, I would say something along the lines of "As much as I want to come home to be with you and the kids, I really think it's important that I figure out my drinking and mental health before that happens." Don't give her the option of telling you no and let her know everything you are doing to make it right (e.g. going to AA, seeing a therapist, etc). I know it's killing you to not be there but just don't push too much on going back home just yet. I'm guessing she wants to see some significant and permanent lifestyle changes before she's comfortable letting you back into their everyday lives.
Good luck, OP. We are all rooting for you.
This. This right here.