You are talking about 2 completely different trips, a one way and interior Alaska travel, and a round trip Seattle cruise.
Sorry, but sail elsewhere if you want a young crowd, ALL Alaska sailings have the bulk of their passengers middle aged and above.
Another sorry, in no way do I think Princess cruisetours are "great". In fact, I would never recommend them for a family. First off, completely point to point, lacking in really seeing Alaska, none go far enough into Denali Park, it also is the most costly way to travel, by at least double for a family. The kids most likely will also be the only ones in your group- think about your above age comment- it is 10 times more likely on the tour portion compared to the cruise. Superior and a far better experience would be to consider going on your own, if you do a one way cruise. Tour interior Alaska with a RV, rental car or if you allow extra time- Alaska RR. (although it does miss all the stops you can make with going by road). The most scenic portion of the Alaska RR is Anchorage/Seward, very convenient if you get a cruise into or out of there. The Anchorage/Talkeetna/Denali Park/Fairbanks section, just about parallels the Parks Highway. So not a bonus to take it.
Significant savings can be had with purchased coupon books.
IF you can not invest at least 2 weeks, then the Pearl is an excellent ship to consider. I sailed both the Pearl and Sun last year. NCL does a good job in Alaska. Freestyle, works great and probably another big plus with a family. Glacier Bay is a gem, with your balcony cabin, IF you want glacier viewing from your cabin, you need a port side.
So do your homework, determine, how much time you have, what your priority is and then sit down and make your plans.
The more you know the better your choices will be for you.