I went on two cruises about 10 years ago, first to the Caribbean and the second to Alaska, both on Royal. As other commenters have said, very different experiences but we LOVED Alaska. It was much less of a party cruise, with a very different demographic, so it was very relaxing. Our stops were Juneau, Skagway, and Victoria. All three were a lot of fun in different ways. Juneau seemed tourist-y and catering to the ships, but we did a zipline tour and the nature was beautiful. Not sure where DCL ports relative to Royal, but there was a small restaurant and shop right near Royal's port where we had lunch and shipped salmon back home because it was so good. Skagway is tiny tiny and definitely a tourist town. We were able to walk around the whole town including visiting pretty much all the shops in under an hour, but it was really cute. Victoria is an actual city so there were plenty to do, also with beautiful gardens. So none of them are like hopping ports in the Caribbean, but still a lot to appreciate. And of course, the glaciers. The nature really is the highlight of the cruise and it's worth it to go just to see all of that, but also sad to see how much has vanished over time. If your kids are into the Instagram-able moments, there are plenty.
I think your kids are a great age to go - that's more or less the target age that I'd like to take my kids. I think mine are a bit too young to really appreciate it right now. There's a lot of history and, yes, nature.
The only things I would be aware of - (1) obviously, the weather. It can get really cold and rainy, but you can pack for that. We wore just sweatshirts on an early morning on deck for a couple of hours watching the glaciers and it was cold but not unbearably cold; (2) we went at the end of the season and it was super rocky one of the sea days - like to the point that they put barf bags all over the ship; (3) because of time zones, the time is changing every 1-2 days.