Welcome to FT!
While Denali is spectacular, having done it with kids of similar ages I'd give it a pass this trip. Not only will lodging be difficult (and expensive) the big issue is in-park logistics. Private cars aren't allowed into the interior of the park, so to get anywhere you have to use shuttle buses. Distances are long, and while there's a good chance you'll see wildlife from the road, it can become very boring and tedious for the kids, and we all know what having antsy kids is like.
So I'd pass on Denali and instead think about a very scenic, very interesting big loop. (I love loop tours as you don't have to retrace your steps. This is an ongoing problem with Alaska, where there are few roads "in" and "out" of most cities.)
Basically, leave Anchorage to the north and take the Glenn Highway to Matanuska Glacier, then continue east to Glennallen, then south to Valdez on the Richardson Highway. The Richardson is one of the most beautiful roads in North America (a real contest when you count some other Alaska and BC highways). Visit Valdez (town okay, surroundings gorgeous) then take the state ferry back across Prince William Sound to Whittier. Head south from Whittier to the Kenai Peninsula (Seward, Homer etc.) for three nights or so, then back to Anchorage.
Here's a Google map.
Note you will need to book the ferry in advance, also confirm with your rental car company that they'll allow it.
http://www.dot.state.ak.us/amhs/
If this is too ambitious, then add a Kenai Fjords cruise out of Seward, for your best shot at seeing numerous marine mammals.
Due to pressure from cruise passengers, I'd shoot for overnights in Seward on weekdays, not the weekend. But you need to get on the stick for accommodations pronto. Staying away from downtown Anchorage is your best bet; having a car will really help.