If it were me in your position - him removing the stash in the closet would be like taking a pebble off a mountain.
My feeling is that he either behaves in a trustworthy manner, or he doesn't. Giving him a list of specific things would not help the trust issue if it were me. Of course, I'm not you, so this is just something to think about.
Trust is something he will earn through his choices and actions, not by crossing things off your list. How about you go see a counselor. I think that would be really helpful. You are going through some major life stress right now. If you already do and I forgot - my apologies.
You are married and living together. I think it is reasonable to expect to know the outcome of the court appearances.
If you want communication sooner rather then later, go see a marriage counselor sooner rather then later. One thing a good marriage counselor will do (especially one familiar with addictions) is help you with communication. For right now watch what he does and listen to what it says.
He knows alcohol is an issue. It wouldn't take much of an IQ to figure out that your wife would want the alcohol out of the house. Not removing it isn't about him not being able to figure it out. It is an action (or lack of action) that he is taking. We can't say where it will lead but in my opinion talking about it won't make any difference even if he does remove it.
People show us who they are by what they do. I was always trying to get my xah to change what he did, thinking it would change who he was. It doesn't really work that way.