Need a little more info -- primarily when you plan to take the trip.
Going the non-cruise route is already a smart move, though it forces you to do a lot of planning.
I'll give you a partial answer on the assumption that your kids' school schedule will force you to take the trip in June, July, or August.
You'll fly into Anchorage (pretty much all flights to Alaska go there). From there, you have all kinds of options. Probably best to take a day to recover from the flight and get your bearings, especially if you have 2 weeks. There are a variety of things to see in and around Alaska. My top recommendation, especially with kids involved, would be the Alaska Native Heritage Center. It does a great job of showing the differences in how the any various tribes lived in Alaska. (I recognize that I've always been into Native Americans. If you have no interest in this, you might ditch this suggestion.) Other options, in random order, a) Anchorage Museum at Rasmuson Center, b) Imaginarium Discovery Center (very popular with kids), c) Point Woronzof (very pretty, some wildlife, d) Wells Fargo History Museum (small but quirky museum). You can google these locations and see what interests you.
Alaska is huge, so you're not going to get to all (or even most) of it in 2 weeks. If you want to see a lot of it, here's what I would suggest. Get in a car, and drive in a modified circle.
My first stop would be a drive up to Denali on Hwy 3. There are some awesome views of Denali along the way. If you're lucky, the mountain will not be shrouded in clouds. There are lots of places to stay outside the National Park. Take the bus ride in to the NP, and hike a bit at one or more of the stops. You should see quite a few animals on the bus, and if you call out that you see a XYZ, they'll usually stop and let you take pics. You also have the option of taking a plane ride over the park, or a helicopter ride to land on Mt. McKinley. Both are fun trips, but also pretty expensive. I would not recommend overnight camping in Denali, even with experienced guides. The trips can be interesting, but they can also be somewhat dangerous (not something I would expose kids to).
From there, I'd continue north on Hwy 3 to Fairbanks. You could stay there, or continue on -- your choice. I forget the location, but there's a road into a state park that is absolutely overrun with moose. It's an awesome experience. I'll see if I can look up what it's called.
Anyway, continue on to Chena Hot Springs Resort. Like most hot springs, it kind of stinks, but it feels great. Your family will enjoy the experience.
Then I'd head south on Hwy 2 to the Wrangell-St. Elias National Park. This is not as popular as Denali or the coastal regions, but it's one of the gems of Alaska. There are some abandoned towns to explore, and some amazing views and wildlife. Check out the web site for the NP, and see if it interests you. If so, try to do one or more of the ranger walks or presentations.
At that point I'd head west toward Anchorage. You could drop down to Valdez, but there are better spots to experience the ocean. There are a few interesting things to do along the way to Anchorage -- just do a little research (I forget the names of them). I'd blow through Anchorage unless you want to spend a night there, and head toward Seward.
I need to take a break here, but will try to post the rest of my suggestions later today.