Hearing Kristen Bell talk about her husband's problems with addiction in the past is heartbreaking. I think that he will remain sober though, because now he has a reason to stay sober. He seems to really love his wife and child, and I hope that their support will be enough to help him stick with these changes.
Although some men "turn around" their lives once they get married and have a family, the process starts with the man himself actually wanting to get sober. Otherwise, you'll have a sober man who is resentful of the person who is making him get sober. That's not a good situation for anybody. Ultimately, Shepard may get sober, but it will be because he wants to, not because of a family.
Kristen Bell tears up while talking about her husband, Dax Shepard. Personally, I don't see how marriage and family will be enough to keep Shepard sober. Alcoholism is the most addictive form of substance abuse, and the only thing that will be able to control him is Dax himself. His family will be hardly a factor in this.
Sobriety is a constant battle, and winning requires more than "marriage and family." While the support that Kristen bell is able to give him will help him on his road to recovery, Shepard will also need counselling and support outside of the home. A good foundation in AA, a sponsor, and a therapist will give him the tools he needs to remain sober.