My first thought was that it would be Sheikh Ismail, the father of the prodigious Mohammad clan: four brothers -
Hanif,
Wazir,
Mushtaq and
Sadiq - played for Pakistan, and that is indeed the Test record. Reggie Ranatunga, a former Sri Lankan government minister, has three Test-playing sons -
Arjuna, Sri Lanka's
former long-serving captain;
Dammika, who was briefly the chief executive of the Sri Lankan board; and
Sanjeewa, while a fourth brother,
Nishantha, played for Sri Lanka in ODIs. But you asked about "international" cricketers, which widens the field beyond just Tests and ODIs, and I think the winner then comes from Ireland. James Joyce has three sons who have played for the Irish national team:
Ed, who has also played for England;
Dominick, who made his ODI debut in the same match as Ed, but for the opposite side (in
this match at Belfast); and
Gus, who
played one first-class match for Ireland in 2000, before they gained full ODI status. But the Joyces also have twin daughters -
Cecelia and
Isobel - who have both played for Ireland's ladies' team. Of course, there might just be someone whose 11 sons all played for Vanuatu, but we haven't got his name yet ...