I welcome you and am glad you are here. I too have been told that we were through. Actually at least once a year I get told this. It used to just tear me up and make me mad and desperate and bring all my abandonment issues to the front. I would tell him he could come home, didn't matter what shape he was in, just as long as I had a body.
Well this year when he pulled his stuff and wrote me the 'I wanna divorce' letter and left, I went to AlAnon. Haven't been in it as long as you, just a few weeks actually. But it has brought me some serenity.
One series of books that I have found really helpful is called "Getting Them Sober." And in these books I have learned that the Addict/alcoholic likes to make us think that they are in charge. That we are dependent on them. When in actuality, it is the other way around. They are very dependent on us. The author states that it is very hard to "lose an alcoholic". Weeks, months, years down the road they reappear, and will try to reenter our lives if we let them. This is true. My father who hasn't spoken to his A X Wife in 20+ years got a call from her the other day to have lunch! So see, they are always around even if they tell you they are done.
I get told the same thing all the time too, that I am so mean. He just can't put up with my meanness anymore. Because I tell him that if he is going to use h he has to go somewhere else. Not here at my house, around my daughter, around me. Every time I make a stand, he tells me we are through. And I guess what I am saying through all this rambling, is he never means it. And neither does yours. If he were through he wouldn't have just stopped by to tuck the kids in, hug and kiss you, blah blah. Like another poster said, he wants his cake and to eat it too. They all do. So you can expect this type of behavior every time you take a firm stand.
What helps me personally get through it, is I picture a little 3 or 4 year old kid standing in the middle of a grocery store aisle and he is pitching a royal fit. I mean he is screaming and yelling to the top of his lungs, he is stomping his feet and jumping up and down and waving his arms all around. He is yelling I hate you mommy, and he might even be pointing at you so there is no mistaking that he is your kid. And he is wanting you to give in. And he is wanting you to react. Even if it is to pop him on the butt, or jerk him up and get in his face and and shake your finger at him and tell him to quit. He wants you to react in some way, ANY WAY, just REACT. And yet, if you just turn your back and start looking at something else, look at the jewelry counter or the pretty towels on the shelves, look at anything, but where this kid can't see your face, just your back. Pretty soon he stops jumping up and down, he stops waving his arms all around, he stops screaming and yelling to the top of his voice, he even stops crying. And as you slowly make your way down the aisle, pretty soon, he pops his thumb in his mouth and follows right along behind you just like nothing happened. And yep, it can be embarrassing. Yep, people are looking at you, thinking in their minds, well if it were me I'd do this, or I'd do that. But they're not you and you're not them. Yep it can be uncomfortable. But it worked. YOU took action, you didn't try to reason, you didn't try to talk sense, you didn't try to bargain or threaten. This kid was beyond all reason, he was beyond all sense, just like a threatening alcoholic addict. Once they see that this kind of behavior does not work with you, that really you could care less (even if you have to fake it), they stop. They stop with the empty silly threats. Doesn't mean they ever stop trying out silly empty threats, they search and search, they never stop trying. And you'll be tired one day and sad, or hungry or just in a weakened state and you'll react. We all do. But then you get back up and brush yourself off and go forward. And the more that you are able to say with your actions 'sorry that just doesn't work with me, but you go ahead and work yourself up into a lather while I walk over here to look at something else' then who knows, it might just be the push that makes him finally get really well. As long as they can keep us upset and talking and defending ourselves and trying to reason with them, they know they are safe. Because as long as we are talking, we are not DOING.
So set your boundaries as to when he can come see the kids. He left, now you can set YOUR rules and boundaries. He doesn't get to have it both ways, oh I'll leave but pop back in whenever. Nope, let him live with his choice. Mine thinks he can leave but pop back in for a booty call whenever the urge hits. No thank you very much. You don't want to put in the day to day you don't get the benefits in my home. I get told the same thing as yours, oh I want to come watch movies with my girls, oh I miss the dogs, oh I need to rake the leaves, oh what ever excuse he can come up with to get over here to see whats going on. Why? Because these are miserable humans! They are not happy! They are in misery and they want every one else to be that way too! They want to look like the good guy, on the outside and do and say things that make us look like the bad guy! They just want to be the good ol' guy and we are the mean mommy. It's what an addict does. They know inside they are no good and what they are doing is no good, but they do everything in their power to make it look just the opposite.
Remember this, addicts/alcoholics don't get with weak women. We are stronger than we give ourselves credit for. We are strong or else we wouldn't have put up with or made it this long. We raise babies, work jobs, manage households, take care of aging parents, feed pets, join PTA, make cupcakes for school, clean our houses all while dealing with an Alcoholic/addicts junk! So baby, you hold your head up high. You don't worry, keep working on yourself and all this other stuff wil sort itself out. When the time is right you will find the questions to your answers. It is a process, and by the time we usually reach out for help we are so sick of the whole situation we just want it to hurry up and get better. We want to get instantly healed. But it just takes time.
Thank you for sharing your story. Please keep coming back. Take a look at the "Getting Them Sober" series of books. Take from them what you need and leave the rest. There is a lot of good info in them. Please keep up with Alanon. Just remember, you are not alone. We are all here for you.

I think one of the biggest mistakes I made in the last 2 weeks of his SUPER DAD/SUPER HUSBAND routine I slept with him. He was over one night doing his SUPER thing and kept on and on and on about crawling in bed together wanting to be with me. I caved in. Now I am emotionally involved again. I wish I hadn't done it.