I am unsure how it is 'your problem' that he doesn't trust you.
I mean I am sure you betrayed him and gave him reason not to trust you, but if he wants to continue in that fashion then that is his choice and there ain't a hell of a lot you can do about except what you are already doing, staying sober focusing on your recovery and acting in a trustworthy manner.
A lot of family member choose not to go to Al Anon because they are too scared to face the fact that they do play a role in the alcoholic relationship. There was probably stuff happening in your relationship, despite how well you thought you hid it, that would trigger alarm bells for most people, but your husband probably choose to ignore it and I would go one step further and say as a child he was probably groomed to ignore it, truth be told. As alcoholics, we're not the only ones who suffer from denial. Even the AA big book says, 'the family is to some extent sick'.
I can understand that you may feel guilty and that it is 'all your fault', but I am also sure God/the higher power has forgiven you and maybe you could work on forgiving yourself too? And continue loving your husband like you are already doing.
At a meeting I use to go to, there was a poster on the wall that said 'God makes all things beautiful in his time.' It's very true.