The father is just as much to blame for his kids death.
In a purely statistical sense, this would appear to be true, which makes everyone saying that drunk driving is "deliberate" murder while the father telling his kids to push the truck is somehow not deliberate murder makes no sense. The reasoning that a lot of overly emotional people are giving here is quite obviously defective.
Now as to which is worse, the driver killing the kids or the father assassinating the driver, it's impossible to say, really. It's comparing apples to oranges, for one thing, and it's contingent upon a whole lot of details that are very murky at the moment as well.
Clearly, the father shouldn't just go putting a bullet through the head of somebody that has killed two of his kids, especially if one of them is still alive and there is another kid with the wife beside that.
I'm not a father, but it seems extremely bizarre to me that he would be focused on revenge that quickly. That being said, it's also pretty obvious that "heat of the moment" laws that give killers leniency make a good bit of sense. Intent, being wronged, being in the moment... all these things matter.
But the sentiment in this thread that anybody who knowingly raises the risk of another person getting killed in any way whatsoever somehow deserves death is just ridiculous. By that logic, anybody who's driven an unsafe jalopy of a car not up to current safety features should also be executed. It's zero tolerance logic at its most absurd level.