First of all, we model behavior that speaks louder than our words. So if we want to encourage our incarcerated loved ones to make healthy changes in their lives, one of the best ways to promote that is to demonstrate changing ourselves.
Secondly, in the end we cannot change anyone else, but we can with God's help, change our own ways of responding to our circumstances. Does a call from a facility result in the same conversation for the 20th time? Do letters read like a litany of "poor me" complaints? Has any of that changed anything? So, if we keep doing what we are doing, we will keep getting what we've got! Keep a note pad by the phone so you can have things to say that are hopeful, and kind. If you are told, "I really don't like my GED instructor." can you be prepared to say, "I know this is hard and I am really proud of you when you keep working on what you can do to plan for a better life." I know I too often wanted to coach, nag, fix, plan when what I really needed to do was be a cheerleader for each baby step.
Thirdly, you can live for another, you can live for yourself or you can live with purpose and love and joy and hope in any circumstance. If you can't claim those things for yourself, how can your incarcerated loved one possibly consider that there is any hope for them. But hope there is, because God is as fully present in prison as he is in the outside world. As you experience this you will bring light into your own world and to your extended family of birth and choice wherever they reside.