Something to keep in mind with AK:
Even when they have the longer hours, the animals tend to go in around the same time. So, after the afternoon parade you'll only want to do the animal-less attractions.
As you've probably noticed, most people suggest leaving after the parade--which means that lines will be shorter then.
Midday breaks can be great, but make sure you've figured out your family. We find that we either need to choose to take a looong break away from the park or a shorter break but remain in the park.
I.e. we might choose what an earlier poster suggested and tour the park until 1 or 2 and then take a 4-5 hour break and go straight to dinner.
Or, we might go to the park at rope drop, tour until about 1, then eat a slow, relaxing lunch. (At AK, pizzafari has airconditioning and interesting rooms and sitting in there for an hour can calm me down and get me ready for more.) With this plan, we'd then hit a few more (high capacity) attractions in the afternoon and plan on an earlier dinner ~6ish.
In picking dinner times, I'd also think about your kids in terms of bedtimes and the return trip from AKL to your resort.
How old are your kids? How late do they normally stay up? Will they nap in the middle of the day (if you take a longer break)? Will a midday nap successfully allow them to stay up later than usual without getting cranky? Etc?
If you've never tried these things, you may want to try some of them as a family experiment sometime before you go to wdw. After all, it'll be easier to learn that a system doesn't work when you are at home than when you are in the middle of the MK.