Alaska is AWESOME, we just went on our second cruise there, first time was with the kids -ages 10 and 15. Go the website for Carnival and read their suggestions for what to pack, etc. Be sure to pack a coat, hat and gloves for everyone; we went in August and the temps are usually in the 60's because you are on the water. When (if) you go to Glacier Bay and College Fjord you are outside on the decks for several hours, and you will absoutely need warm clothing. It's not the 'sit-around-the-pool-and-sunbathe' kind of cruise; but you won't find any better scenery.
For daytime just dress casually, t'shirts and jeans. For dinner they suggest "resort casual", or what I would call Business Casual, slacks (not jeans) or a casual dress. You will have one or two formal nights, which are more dressy; for men a sport coat/suit (not many wear a tux) and for women a dressy suit/dress or evening gown (avoid the prom dress look). Those are the nights you will want to have famiy pictures taken (they will have several different photographers set up with different backgrounds, check them all out and then pick which background you want). Warning -- they will take your pictures everywhere -- the first is on arrival, then at dinner several nights, around the decks and often as you leave the ship for your shore excursions, etc. (you have NO obligation to buy any of them, but you will want to buy them all, so set up a budget). Speaking of shore excursions -- go on-line and book your shore excursions well in advance, the popular ones sell out quickly. You can always cancel or change them when you get on board. You will want to pick excursions that are appropriate for your kids ages. For instance, the horseback rides have a minimum age requirement which is 9 or 10. Also remember that even though you are going in a group, you don't need to joined at the hip and do absoutlely everything together -- it's ok to do separate shore excursions. On one cruise, my daughter & I kissed the dolphins, and my son and husband went racing on one of the America's Cup sailboats. I can't remember if Carnival (we usually do Princess or Royal Caribbean) has the anytime seating, if they do you can go to dinner at any time you want. If they do 1st & 2nd seating, pick the first seating and then go to the shows. The second seating makes dinner quite late for the younger kids. Every night you will receive your "Carnival Capers" newsletter that lists everything going on around the ship the next day so you can plan out what activities you want to do. Make sure you check out the Kid's Clubs -- special programs set up for the kids (the 2 year old may be too young) so you can drop them off, they have fun playing games/crafts, etc. and you can play bingo or do whatever you want, and they have their own newsletter. One of the cruise lines gives the parents a pager in case they need you. You might also want to take walkie talkies to make staying in touch a little easier if everyone is doing different things on the ship. Our cell phones worked when we were close to the shore, but didn't work in College Fjord (check with your cell carrier to see if you will have roaming charges or not). There is a lot to do, but you'll need to plan down-time for the kids also so you don't overtire them. Finally, make sure you fill out the registration stuff on-line so that check-in at the ship will be quick & easy. Have fun and enjoy all that Alaska has to offer!!!