IMO trust is earned by building a track record of trust worthy behavior. He isn't there yet. You get to decide when his track record is long enough for you to trust him again. He's got a long ways to go.
Please consider postponing the wedding until you have this sorted out. Marriage complicates things enormously.
He is an alcoholic. There can be peaks and valleys but alcoholics can not moderate their drinking. My xah had many peaks where he really cut back on his drinking for whatever reason (new baby, job, house, some event) but when he slid back down into that valley it was a little deeper each time.
One things is for sure - alcoholism always progresses unless the alcoholic stops drinking forever.
ETA: Welcome to the group! There is so much support here. Stick around and I really got a lot out of the stickies at the top of the forum so if you have read them yet, check them out.