Let the adults go to Palo. Trust me, the 16 yr. will be able find something to eat and do for and hour. There were times when my then ds-13 begged not to go to dinner with us.
Yes, they are very strict about the age in all adult areas as they should be. This is one of the reasons we go back.
Most cruiselines have adult areas, but they do not enforce the rules. When you let just one bend the rules, you have to let all the others too.