If you are comfortable driving, remember Alaska is still in the US. Pretty much every port has a rental car office nearby, and you can tour around on your own for about $100 plus the gas.
The only tricky excursion to DIY in a rental is the White Pass train. Fortunately, we had enough adult drivers that we split the party into two. One took the train up and drove the car down, and the other did it in reverse. It was great. Plenty of photo stops as we liked - including the Emerald Lake - and we actually drove all the way to Whitehorse (in Yukon) to grab a quick bite before turning around.. Just the $100 rental plus gas plus cost of the train tickets.
If you wanted to save more, you could also just do the drive (and skip the train). The road and the train share a large part of the same path.
Here is a checklist of all major saving ideas if you are sailing with Disney:
1. Book on the opening day with a placeholder.
2. Book through a TA that nets you a good credit or rebate like Costco.
3. Sail in an inside cabin - category 11, for instance - and make use of the top deck for looking out.
4. Use a credit card that gets you either enough points for your flights (Amex is our favorite) or a cash back as a rebate.
5. If you can't book on the opening day, book when you can with the placeholder - or wait till inside the cancellation penalty for discounted rates.
Specifically for Alaska:
6. Sail in May or September, the shoulder season.
7. Do excursions on your own, using a rental car or directly with an operator.
8. You could skip the excursions altogether - except for the one you really want - and do most of your sightseeing from water and in the ports. The most scenic part of this cruise will still be the glacier day and when the ship is sailing through the Inside Passage.
9. Do an adults-only excursion. Leave the kids in the clubs for the day, and venture out on your own. Think of it as your 'me' or 'us' time. No guilty feeling. Once the kids have made their friends in the clubs, it's not about mountains and glaciers anymore.
10. Don't try to do everything. Maybe not with kids, but
you will be back. Keep some sightseeing for the return trip whenever that might be.