Here is some advice that I hope you find helpful:
1. Layering is the key in Alaska. The weather can change sooooo quickly there! Pack t-shirts, sweatshirts, a light jacket. If your family is planning to eat in some of the pay-extra restaurants, pack a couple of skirts or nice pants. You don't have to dress real fancy - just resort casual. They have one optional formal night on the Norwegian Star, so you might want to bring one fancy item. Keep in mind that comfort is everything! Sweatpants are great for outdoor excursions.
2. I owe a big thanks to one lady who offered the most wonderful piece of advice that, thankfully, we listened too. We went to Walmart and bought a rain poncho (less than $3.00) to go over our light jackets. Not only did it keep out rain, but also wind! It can get quite windy in some ports. When it does rain, however, it usually doesn't last long.
3. We just got back from the Star on the Alaskan cruise on June 6th, so please feel free to e-mail me if you have any questions.
Hope this helps - and have a wonderful time! Alaska is so beautiful, you are sure to have an awesome trip!