A couple of things stood out to me.
First - remind yourself of the three C's. Find a way to believe these, right down to your core.
You did not cause his alcoholism (or recovery or relapse).
You can not control his alcoholism (or recovery or relapse).
You can not cure his alcoholism (or recovery or relapse).
You have your own answers - they are right there in your post. Your peace and serenity come from no contact with the manipulative ex......and he is being VERY manipulative. The contact is hurting you and not helping him. It is the same old merry go round.
When you find a way to believe those 3 c's you'll be able to let go.
ETA: My xah says that stuff all the time. He has been sober for four weeks and now he is over come with anxiety 24/7, quit a job, wants to move in with me, has no where to go and nothing to do - all because he doesn't have his family and to hear him tell it - I can suddenly fix everything. Believe those three c's - it will set you free.
As far as contact we correspond by email 99% of the time and I do not respond to anything that is not child related. When we are together face to face during kid activities we are civil of course and I walk away if he tries to talk about something not kid related or chit chat stuff. He had the kids put me on the phone over thanksgiving (which is when the above was revealed) and I simply told him to go to an AA meeting - which of course he did not do because he says he no longer has a drinking problem - he hasn't drank in 4 weeks. This is man that drank every day for at 20 years. Same old same old. Nothing I do will make any difference at all and I really and truely believe that and my job is to protect my home - the one I live in and the one in my head.