In a family, there are 3 fathers, 3 mothers, 3 daughters, 3 sons, 2 nieces, 2…

Answer: 10 members (minimum).

Construction (one minimal arrangement):

• Grandfather (male) — father of the son and the daughter.

• Grandmother (female) — mother of the son and the daughter.

• Son (male) — child of the grandparents; married to his wife; father of two children.

• Son's wife (female) — mother of the son's two children; she is the daughter-in-law (one daughter-in-law).

• Daughter (female) — child of the grandparents; mother of two children.

• Daughter's husband (male) — father of the daughter's two children; he is the son-in-law (one son-in-law).

• Four grandchildren: two boys and two girls (the son's two children and the daughter's two children).

Counting roles in this 10-person family:

• Fathers (3): Grandfather, the son (parent of two grandchildren), and the daughter's husband (parent of two grandchildren).

• Mothers (3): Grandmother, the son's wife, and the daughter.

• Sons (3): the son (child of grandparents) and the two grandsons.

• Daughters (3): the daughter (child of grandparents) and the two granddaughters.

• Nieces (2) and Nephews (2): the grandchildren are nieces/nephews to their aunt/uncle (the daughter and the son respectively) — two of each gender among the four grandchildren.

• Son-in-law (1): the daughter's husband; Daughter-in-law (1): the son's wife.

Thus all listed relationships are satisfied with exactly 10 distinct family members, so the minimum number is 10.