My days and schedules are flexible! Here is just my rough draft:

Day 1 ~ 3 : having fun in Anchorage, we can enjoy good meals together and do a winter hiking in a state park.

Day 4 : A Saturday. Can take the aurora train from Anchorage to Fairbanks. (from 8:30 to 20:00) and then go to chena hot spring hotel.

Day 5 ~ 7 : Dog sledding, dog petting, hot spring maybe with aurora view and other winter activities provided from the hotel.