How does a addict who is in a committed relationship win back trust?

You can't win back trust. As you said, you cannot take it for granted that you will take 'all measures necessary' to keep your life in line. Do you think it is easy for an alcoholic to win back trust? Or a drug addict? They know that trust is not something to be won back. Just as they struggle to keep sober/straight, the people around them face a constant struggle to trust them. I'm sorry. Life's not easy. But there are sober people and there are straight peole with their problems so far behind them that they lead lives free of those kinds of problems. They know they can never relax and give an inch to temptations, however.