D.K.
Cruises can be a lot of fun! Every day the ship is at sea there will be lots of on board activities that are free, so make sure to pick a few to do. Some of the cruises will give you points or dollars if you do any of the physical activities and at the end you can trade them in for t-shirts, etc. There are usually lots of activities and contests to choose from and some of the contests are fun to watch even if you don't participate. I would check out the excursion list for Cozumel and find something that appeals to all of you and book in advance, since sometimes they fill up quickly.
I've done two cruises that were family celebrations/reunions (and I'm one of the grandkids). We all did our own thing during the day, usually in small groups then at night we all met up for dinner in the main restaurant. The food was always great there and it was fun dressing up some of the nights and letting everyone catch up. A cruise was a perfect way for everyone to get a chance to do what they wanted, but also to see family and spend some time together.
You will have your picture taken many times throughout the cruise by the cruise staff, if you plan on buying any of the pictures they usually go on sale at the end or there are deals where you can get more than one. We usually just took our own or had someone else take one of us, but we did get a big family picture on formal night.
Good luck and have a great time with your kids! It will be a wonderful trip for all of you.