OP, if you are going to Alaska listen to what PP's said, Princess. They have the nicest itineraries if you are wanting to really see Alaska. If you care more about the ship and what if offers, then that can sway my opinion.
Who told you it was mainly old people, Carnival cruisers? Take that with a grain of salt. Princess is owned by Carnival. Just like Celebrity is owned by Royal Caribbean. Princess and Celebrity is the upgrade, but it has a vast appeal among ages. The ship isn't full of 80 year olds in wheelchairs waiting for bingo and pudding.
You need to research and see what cruise line would best suit your family. There are so many
YouTube videos going though the different cruise lines. Pick which 3 you think would work for your family then start watching videos to decide. And make sure when you decide on which cruise line to then find out the specific ship!
What works for one family may not work for another. All depends on what you find important. And that can vary wildly.
If you are still on the fence about Princess, then my next suggestion would be Royal Caribbean or NCL. Personally, Disney is nice, but for that price tag I would chose Celebrity. But again, that is just my opinion.
Since you are asking, I am telling you Carnival would be my last choice.
I highly recommend Celebrity although I don't know if they have Alaska trips. Carnival is more of a party ship. If you want to party then Carnival is the place to go. By the way 40 is hardly old. When you get to 75 you will know just how young that was.
They do. I have been on 3 of them.

I love X!