Please read the other threads in this forum. Nearly the exact same question has been asked several times recently, and I've provided detailed info on my trip last summer with my 8 and 13 yr old.

Cut and past from my itinerary/planning document of what I'd recommend:

Alaska Native Heritage Center
Matanuska Glacier Ice Fall Trek
Reindeer Farm - Palmer
Iditarod Headquarters - Wasilla (only if it's on the way)
26 Glacier Tour - Whittier
Portage Glacier - hikes in the area, including Portage Pass, while you're on the Whittier side and Byron Glacier Trail on lake side
Kayak Resurrection Bay - Kayak Adventures Worldwide
Seavey's IdidaRide Sled Dog Tours
Exit Glacier hike
Alaska Sea Life Center
Alaska Wildlife Conservation Center

This is mostly in Anchorage area, plus a couple of nights in Seward.

We had 2 more days, but I left off our 2 day trip to Talkeetna and Denali, so this should easily fill your time, if not more. Denali was nice, but I don't recommended trying to squeeze it in with your time available.

Anchorage has hotels, so that shouldn't be a problem. We stayed at the Spring Hill Suites by the University. A bot away from town, but a great place for a family. Seward is more challenging, especially this late. We stayed at a B&B - you may want to start your planning there, see if/when you can find 2 consecutive nights, and plan travel around that. We stayed at the Havenwood House - very nice, but they were nearly booked up when we made plans in about February.