We have sailed on both
DCL and NCL in Alaska and loved both cruises, though for different reasons. NCL had the best itinerary (for us) as we wanted a one way cruise that allowed us to spend time in mainland Alaska, which we absolutely loved. The DCL one was, well, a
Disney cruise - so yeah, we loved it. Alaska was spectacular, as well, but we didn't get to go to Glacier Bay or Hubbard Glacier which we did with NCL (DCL does offer a few Hubbard Glacier cruises on occasion).
That being said, I'll try my best to answer your questions.
1. Food is subjective. We all have different tastes. For us, hands down, NCL was better. We loved the variety of the restaurants and felt overall the food just tasted better than on DCL. Disney food isn't bad, it's just kind of bland and unimaginative for our palate. Others will disagree with me, and they won't be wrong. We all just like different things. On NCL there is no assigned dining rotation. You eat where and when you choose, which we
love. Others don't care for that because it does require some preplanning and making reservations ahead of time. That doesn't bother me and I greatly prefer it to DCL's assigned rotations and tables.
2. I can't speak to the kid's club as our son was 19 at the time we sailed NCL. I will say this, though, NCL isn't even in DCL's universe when it comes to being kid-friendly. There is a reason we waited until our son was 19 to try them. The shows are definitely geared for adults, and some are completely inappropriate for children (though this will be clearly stated in the Dailies). If you take one of the new ships, though - Bliss or Joy they do have a lot of things for older kids - go karts ($$), laser tag ($$), virtual reality games ($$), some really big water slides, etc. NCL is definitely trying to move to a lot more family oriented activities on their new ships, I believe. If you are on one of the older ships, there will be a sports court, but that's about it (maybe an arcade??). You didn't say how old your kids were, but I'd recommend really checking out any NCL ship you are interested in to see if there is anything your kids would enjoy.
3. Are you making a mistake? I can't answer that. You said you are a die-hard Disney fan, so I'll say this. Unless you are totally committed to forgetting about Disney for this trip and just focus on a wonderful cruise to Alaska, then yes, you probably are. But if you go into it with an open mind and get excited about all of the wonderful things you'll see in Alaska, then I think you can have a great time. We were a bit nervous to stray away from the Mouse. But our last two cruises have now been on NCL, as will our next two upcoming. So obviously, we enjoy it. But all of those were taken with just adults. YMMV.