I'm the family cruise editor here. Actually we've been to Seven Mile Beach on two different cruises and had no problem using the beach facilities for the day. While I don't remember which beach club areas we swam at, you can ask the shore excursions staff of your cruise ship. Also, the cab drivers known which beaches accept day visitors. You will have to pay a few dollars per person to use the beach chairs, etc. There are plenty of watersports rentals along the beach which should keep your crew of teens busy!
In Jamaica, I strongly suggest going on a shore excursion sold through the cruise line. While I'm usually a big advocate of going out on your own to explore, I think you'd be better off in Jamaica to choose a group tour. Jamaicans are friendly but sometimes too friendly and you may feel intimidated on your own to buy their goods, etc. Dunns River Falls is a big favorite -- you climb the waterfalls as a group.
I hope this helps.
Smooth sailing,
Luisa Frey GAynor