We get past the "trust factor" by staying sober and being truthful.
In my case it tooks years for my family to become not trustful, and although I have their total support, I am prepared to spend as much time regaining their support. However, I will not be defensive nor hurt when challenged, but simply state the honest to goodness truth. While it will take them some time to believe it, I will, and that is what is sooooo important to me right now.