A misbehaving child mimics their environment and upbringing. Frankly, the child might be the offspring of drunken parents who are so self absorbed that they fail to exercise their parental responsibility.
The issue with a drunk can best be served by alerting a member of the cruise staff to intervene. The issue with a child is complicated by what others have stated concerning being "PC" and the potential legal issues.
I have, and will probably continue to have, experience with drunks and children behaving badly in public. The experience is magnified by the confined environment of a cruise ship. I look forward to the poster who supplies the best answer on how to handle the issue!