This is a perceptive question. There are, indeed, two rounds in the lottery. In the first round, the head of the family draws. This purpose of this round is to determine which family is chosen for the ritualistic stoning. Once this is established, there is another round. In this second round, there is another drawing among the family members with one exception. Daughters draw with the husband's family. Here are the words of Mr. Summers. It is actually repeated twice.
"Daughters draw with their husbands' families, Tessie," Mr. Summers said gently. "You know that as well as anyone else."
The second drawing is important to the story, because we really begin to see fear. When the Hutchinson's "win" the lottery, fear grips the family. The Hutchinson family has five eligible people: Bill (the father), Tessie (the mother), and three children: Bill junior, Nancy, and Dave.
The very fact that children are included in the lottery shows the utter barbarity of the lottery. At the time of drawing, a little girl whispers:
"I hope it's not Nancy..."
The scene is tense. When it is revealed that Tessie is chosen, the other family members are relieved and the children are filled with laughter.
The second drawing brings home the utter evilness of the lottery. It brings out the worst in people.