Family is turned on its head in the prison camp. All the zeks in One Day in the Life of Ivan Denisovich are separated from their families in the real world, some for decades. In fact, there is so much time and space between families that they almost cease to operate as such. Shukhov's relationship with his wife and his children seems almost meaningless in the camps; he's largely disconnected from them. Shukhov can scarcely understand their experiences since he's been away, and they probably can't understand his life either. Other zeks have completely lost their families, like Tyurin, or have been abandoned by their families, like Fetyukov. In the camp, new families form and the work gangs start operating as a type of family, albeit a cutthroat mafia family.
Shukhov is definitely the brains of his camp "family," and he might be the most valuable member of his gang.
The role of father figure in the gang seems to shift around and depends on which characters are interacting at the time.