According to a University of Florida study, Parents play a powerful role in predicting DUI:

for parents, even moderate drinking can result in one unintended consequence: an increased risk their children will drive under the influence as adults. . . . Writing in the current issue of the journal Accident Analysis and Prevention, University of Florida researchers found that about 6 percent of adolescents whose parents drank even sporadically reported driving under the influence at age 21, compared with just 2 percent of those whose parents did not imbibe.

I'm not sure if I completely buy this connection. The thrust of the article is that if a parent takes a drink, then the kid's chances of driving drunk increase by 4 percentage points. It seems to me that making this correlation minimizes the many other factors involved in the decision to drive drunk. Speaking personally, the times in my youth when I drove after having too much to drink had nothing to do with my parents, who drank sparingly [father] and never [mother].

Now, I do believe that a child who is raised in a household where drinking is a normal and regular part of the day is more likely to be a drinker in the same vein as the parent. Environmental factors count. Intuitively, however, taking that generality and applying it to drinking parents causing drunk driving may be a stretch.