Following with interest, and keeping everything crossed for you OP.
It must be hard as he's finally making the effort to stay sober, which is bound to make you question yourself. In some ways the leaving would be much easier if he'd already fallen off the wagon again, but I think you need to follow through with your plans, for your own sake and the future of your children.
No doubt he will go on a downward spiral and use your leaving as the excuse to play the victim and guilt trip you as much as possible. I would think about leaving him a carefully worded letter, including something along the lines of:
"I know you've been trying really hard to stay off drink and drugs, and you are trying to make a new start, but weighing that up against the years of previous drinking/[insert any relevant bad behaviour here] that you've put me and the children through, and all the previous times you've tried and failed to turn over a new leaf, I'm not willing to invest any more years in this marriage. I really hope you manage to beat your addictions, but I believe you need professional help to do it, rather than me enabling you to continue your drinking/drug taking lifestyle. I hope that in time we can be friends, and co parent our children, but for the sake of my own health I can no longer endure living with an alcoholic."
I'm sure my words are far from perfect, but I'm trying to find words that might give your STBexDH a small glimmer of hope that you would be willing to be a supportive friend from a distance if he turned over a new leaf, rather than the message that you have completely hardened your heart towards him. (Although maybe you will have to do that, in time, to survive all this. Only you know that.) I'll be rooting for you and waiting for your update next week... maybe next Friday you will post from your new home.